Scattering of a high-order Bessel beam by a spheroidal particle

Science.gov (United States)

Han, Lu

2018-05-01

Within the framework of generalized Lorenz-Mie theory (GLMT), scattering from a homogeneous spheroidal particle illuminated by a high-order Bessel beam is formulated analytically. The high-order Bessel beam is expanded in terms of spheroidal vector wave functions, where the spheroidal beam shape coefficients (BSCs) are computed conveniently using an intrinsic method. Numerical results concerning scattered field in the far zone are displayed for various parameters of the incident Bessel beam and of the scatter. These results are expected to provide useful insights into the scattering of a Bessel beam by nonspherical particles and particle manipulation applications using Bessel beams.

Coherence of the vortex Bessel-Gaussian beam in turbulent atmosphere

Science.gov (United States)

Lukin, Igor P.

2017-11-01

In this paper the theoretical research of coherent properties of the vortex Bessel-Gaussian optical beams propagating in turbulent atmosphere are developed. The approach to the analysis of this problem is based on the analytical solution of the equation for the transverse second-order mutual coherence function of a field of optical radiation. The behavior of integral scale of coherence degree of vortex Bessel-Gaussian optical beams depending on parameters of an optical beam and characteristics of turbulent atmosphere is particularly considered. It is shown that the integral scale of coherence degree of a vortex Bessel-Gaussian optical beam essentially depends on value of a topological charge of a vortex optical beam. With increase in a topological charge of a vortex Bessel-Gaussian optical beam the value of integral scale of coherence degree of a vortex Bessel-Gaussian optical beam are decreased.

Integral momenta of vortex Bessel-Gaussian beams in turbulent atmosphere.

Science.gov (United States)

Lukin, Igor P

2016-04-20

The orbital angular momentum of vortex Bessel-Gaussian beams propagating in turbulent atmosphere is studied theoretically. The field of an optical beam is determined through the solution of the paraxial wave equation for a randomly inhomogeneous medium with fluctuations of the refraction index of the turbulent atmosphere. Peculiarities in the behavior of the total power of the vortex Bessel-Gaussian beam at the receiver (or transmitter) are examined. The dependence of the total power of the vortex Bessel-Gaussian beam on optical beam parameters, namely, the transverse wave number of optical radiation, amplitude factor radius, and, especially, topological charge of the optical beam, is analyzed in detail. It turns out that the mean value of the orbital angular momentum of the vortex Bessel-Gaussian beam remains constant during propagation in the turbulent atmosphere. It is shown that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam propagating in turbulent atmosphere calculated with the "mean-intensity" approximation is equal to zero identically. Thus, it is possible to declare confidently that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam in turbulent atmosphere is not very large.

Generating and measuring non-diffracting vector Bessel beams

CSIR Research Space (South Africa)

Dudley, Angela L

2014-03-01

Full Text Available We demonstrate how to create non-diffracting vector Bessel beams by implementing a spatial light modulator (SLM) to generate scalar Bessel beams which are then converted into vector fields by the use of an azimuthally-varying birefringent plate...

Higher-order harmonics of general limited diffraction Bessel beams

International Nuclear Information System (INIS)

Ding De-Sheng; Huang Jin-Huang

2016-01-01

In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m -th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. (special topic)

Techniques to sort Bessel beams

CSIR Research Space (South Africa)

Dudley, Angela L

2013-09-01

Full Text Available -polar coordinate transformation, translating helically phased beams into a transverse phase gradient. By introducing two cylindrical lenses we can focus each of the azimuthal modes associated with each Bessel beam to a different lateral position in the Fourier...

Laser-driven acceleration with Bessel and Gaussian beams

International Nuclear Information System (INIS)

Hafizi, B.; Esarey, E.; Sprangle, P.

1997-01-01

The possibility of enhancing the energy gain in laser-driven accelerators by using Bessel laser beams is examined. Scaling laws are derived for the propagation length, acceleration gradient, and energy gain in various accelerators for both Gaussian and Bessel beam drivers. For equal beam powers, the energy gain can be increased by a factor of N 1/2 by utilizing a Bessel beam with N lobes, provided that the acceleration gradient is linearly proportional to the laser field. This is the case in the inverse free electron laser and the inverse Cherenkov accelerators. If the acceleration gradient is proportional to the square of the laser field (e.g., the laser wakefield, plasma beat wave, and vacuum beat wave accelerators), the energy gain is comparable with either beam profile. copyright 1997 American Institute of Physics

Optical tractor Bessel polarized beams

Science.gov (United States)

Mitri, F. G.; Li, R. X.; Guo, L. X.; Ding, C. Y.

2017-01-01

Axial and transverse radiation force cross-sections of optical tractor Bessel polarized beams are theoretically investigated for a dielectric sphere with particular emphasis on the beam topological charge (or order), half-cone angle and polarization. The angular spectrum decomposition method (ASDM) is used to derive the non-paraxial electromagnetic (EM) field components of the Bessel beams. The multipole expansion method using vector spherical harmonics is utilized and appropriate beam-shape coefficients are derived in order to compute the radiation force cross-sections. The analysis has no limitation to a particular range of frequencies such that the Rayleigh, Mie or geometrical optics regimes can all be considered effectively using the present rigorous formalism. The focus of this investigation is to identify some of the tractor beam conditions so as to achieve retrograde motion of a dielectric sphere located arbitrarily in space. Numerical computations for the axial and transverse radiation force cross-sections are presented for linear, right-circular, radial, azimuthal and mixed polarizations of the individual plane waves forming the Bessel beams of zeroth- and first-order (with positive or negative helicity), respectively. As the sphere shifts off the beam's axis, the axial pulling (tractor) force is weakened. Moreover, the transverse radiation force cross-section field changes with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on the choice of ka and the half-cone angle α0. These results are particularly important in the development of emergent technologies for the photophoretic assembly of optically-engineered (meta)materials with designed properties using optical tractor (vortex) beams, particle manipulation, levitation and positioning, and other applications.

Scattering of linearly polarized Bessel beams by dielectric spheres

Science.gov (United States)

Shoorian, Hamed

2017-09-01

The scattering of a Linearly Polarized Bessel Beam (LPBB) by an isotropic and homogenous dielectric sphere is investigated. Using analytical relation between the cylindrical and the spherical vector wave functions, all the closed- form analytical expressions, in terms of spherical wave-functions expansions, are derived for the scattered field. It is shown that in the case of conical angle of incident Bessel beam is equal to zero, the Linearly Polarized Bessel Beam becomes a plane wave and its scattering coefficients become the same as the expansion coefficients of plane wave in Mie theory. The transverse Cartesian and spherical components of the electric field, scattered by a sphere are shown in the z-plane for different cases, moreover the intensity of the incident Bessel beam and the effects of its conical angle on the scattered field and the field inside the sphere are investigated. To quantitatively study the scattering phenomenon and the variations of the fields inside and outside of the sphere, the scattering and absorption efficiencies are obtained for the scattering of the linearly-polarized Bessel beam, and are compared with those of the plane wave scattering.

Higher-order harmonics of general limited diffraction Bessel beams

Science.gov (United States)

Ding, De-Sheng; Huang, Jin-Huang

2016-12-01

In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074038 and 11374051).

Microwave bessel beams generation using guided modes

KAUST Repository

Salem, Mohamed

2011-06-01

A novel method is devised for Bessel beams generation in the microwave regime. The beam is decomposed in terms of a number of guided transverse electric modes of a metallic waveguide. Modal expansion coefficients are computed from the modal power orthogonality relation. Excitation is achieved by means of a number of inserted coaxial loop antennas, whose currents are calculated from the excitation coefficients of the guided modes. The efficiency of the method is evaluated and its feasibility is discussed. Obtained results can be utilized to practically realize microwave Bessel beam launchers. © 2006 IEEE.

Microwave bessel beams generation using guided modes

KAUST Repository

Salem, Mohamed; Kamel, Aladin Hassan; Niver, Edip

2011-01-01

A novel method is devised for Bessel beams generation in the microwave regime. The beam is decomposed in terms of a number of guided transverse electric modes of a metallic waveguide. Modal expansion coefficients are computed from the modal power orthogonality relation. Excitation is achieved by means of a number of inserted coaxial loop antennas, whose currents are calculated from the excitation coefficients of the guided modes. The efficiency of the method is evaluated and its feasibility is discussed. Obtained results can be utilized to practically realize microwave Bessel beam launchers. © 2006 IEEE.

Self-healing of Bessel-like beams with longitudinally dependent cone angles

International Nuclear Information System (INIS)

Litvin, I; Burger, L; Forbes, A

2015-01-01

Bessel beams have been extensively studied, but to date have been created over a finite region inside the laboratory. Recently Bessel-like beams with longitudinally dependent cone angles have been introduced allowing for a potentially infinite quasi non-diffracting propagation region. Here we show that such beams can self-heal. Moreover, in contrast to Bessel beams where the self-healing distance is constant, here the self-healing distance is dependent on where the obstruction is placed in the field, with the distance increasing as the Bessel-like beam propagates farther. We outline the theoretical concept for this self-healing and confirm it experimentally. (paper)

Coherence degree of the fundamental Bessel-Gaussian beam in turbulent atmosphere

Science.gov (United States)

Lukin, Igor P.

2017-11-01

In this article the coherence of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is analyzed. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian optical beam of optical radiation. The behavior of a coherence degree of a fundamental Bessel-Gaussian optical beam depending on parameters of an optical beam and characteristics of turbulent atmosphere is examined. It was revealed that at low levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam has the characteristic oscillating appearance. At high levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam is described by an one-scale decreasing curve which in process of increase of level of fluctuations on a line of formation of a laser beam becomes closer to the same characteristic of a spherical optical wave.

Photoacoustic transformation of Bessel light beams in magnetoactive superlattices

Energy Technology Data Exchange (ETDEWEB)

Mityurich, G. S., E-mail: George-mityurich@mail.ru [Belarusian Trade and Economics University of Consumer Cooperatives (Belarus); Chernenok, E. V.; Sviridova, V. V.; Serdyukov, A. N. [Gomel State University (Belarus)

2015-03-15

Photoacoustic transformation of the TE mode of a Bessel light beam (BLB) has been studied for piezoelectric detection in short-period superlattices formed by magnetoactive crystals of bismuth germanate (Bi{sub 12}GeO{sub 20}) and bismuth silicate (Bi{sub 12}SiO{sub 20}) types. It is shown that the resulting signal amplitude can be controlled using optical schemes of BLB formation with a tunable cone angle. A resonant increase in the signal amplitude has been found in the megahertz range of modulation frequencies and its dependences on the BLB modulation frequency, geometric sizes of the two-layer structure and piezoelectric transducer, radial coordinate of the polarization BLB mode, and dissipative superlattice parameters are analyzed.

Higher-order harmonics of limited diffraction Bessel beams

Science.gov (United States)

Ding; Lu

2000-03-01

We investigate theoretically the nonlinear propagation of the limited diffraction Bessel beam in nonlinear media, under the successive approximation of the KZK equation. The result shows that the nth-order harmonic of the Bessel beam, like its fundamental component, is radially limited diffracting, and that the main beamwidth of the nth-order harmonic is exactly 1/n times that of the fundamental.

Optical trapping with Bessel beams generated from semiconductor lasers

International Nuclear Information System (INIS)

Sokolovskii, G S; Dudelev, V V; Losev, S N; Soboleva, K K; Deryagin, A G; Kuchinskii, V I; Sibbett, W; Rafailov, E U

2014-01-01

In this paper, we study generation of Bessel beams from semiconductor lasers with high beam propagation parameter M 2 and their utilization for optical trapping and manipulation of microscopic particles including living cells. The demonstrated optical tweezing with diodegenerated Bessel beams paves the way to replace their vibronic-generated counterparts for a range of applications towards novel lab-on-a-chip configurations

Acoustic manipulation: Bessel beams and active carriers

Science.gov (United States)

Rajabi, Majid; Mojahed, Alireza

2017-10-01

In this paper, we address the interaction of zero-order acoustic Bessel beams as an acoustic manipulation tool, with an active spherical shell, as a carrier in drug, agent, or material delivery systems, in order to investigate the controllability of exerted acoustic radiation force as the driver. The active body is comprised of a spherical elastic shell stimulated in its monopole mode of vibrations with the same frequency as the incident wave field via an internally bonded and spatially uniformly excited piezoelectric actuator. The main aim of this work is to examine the performance of a nondiffracting and self-reconstructing zero-order Bessel beam to obtain the full manipulability condition of active carriers in comparison with the case of a plane wave field. The results unveil some unique potentials of the Bessel beams in the company of active carriers, with emphasis on the consumed power of the actuation system. This paper will widen the path toward the single-beam robust acoustic manipulation techniques and may lead to the prospect of combined tweezers and fields, with applications in delivery systems, microswimmers, and trapper designs.

Engineering the on-axis intensity of Bessel beam by a feedback tuning loop

Science.gov (United States)

Li, Runze; Yu, Xianghua; Yang, Yanlong; Peng, Tong; Yao, Baoli; Zhang, Chunmin; Ye, Tong

2018-02-01

The Bessel beam belongs to a typical class of non-diffractive optical fields that are characterized by their invariant focal profiles along the propagation direction. However, ideal Bessel beams only rigorously exist in theory; Bessel beams generated in the lab are quasi-Bessel beams with finite focal extensions and varying intensity profiles along the propagation axis. The ability to engineer the on-axis intensity profile to the desired shape is essential for many applications. Here we demonstrate an iterative optimization-based approach to engineering the on-axis intensity of Bessel beams. The genetic algorithm is used to demonstrate this approach. Starting with a traditional axicon phase mask, in the design process, the computed on-axis beam profile is fed into a feedback tuning loop of an iterative optimization process, which searches for an optimal radial phase distribution that can generate a generalized Bessel beam with the desired onaxis intensity profile. The experimental implementation involves a fine-tuning process that adjusts the originally targeted profile so that the optimization process can optimize the phase mask to yield an improved on-axis profile. Our proposed method has been demonstrated in engineering several zeroth-order Bessel beams with customized on-axis profiles. High accuracy and high energy throughput merit its use in many applications.

Optical force exerted on a Rayleigh particle by a vector arbitrary-order Bessel beam

International Nuclear Information System (INIS)

Yang, Ruiping; Li, Renxian

2016-01-01

An analytical description of optical force on a Rayleigh particle by a vector Bessel beam is investigated. Linearly, radially, azimuthally, and circularly polarized Bessel beams are considered. The radial, azimuthal, and axial forces by a vector Bessel beam are numerically simulated. The effect of polarization, order of beams, and half-cone angle to the optical force are mainly discussed. For Bessel beams of larger half-cone angle, the non-paraxiality of beams plays an important role in optical forces. Numerical calculations show that optical forces, especially azimuthal forces, are very sensitive to the polarization of beams. - Highlights: • Optical force exerted on a Rayleigh particle by a vector Bessel beam is analytically derived. • Radial, azimuthal, and axial forces are numerically analyzed. • The effect of polarization, order of beam, and non-paraxiality is analyzed.

Talbot self-imaging phenomenon under Bessel beam illumination

Science.gov (United States)

Chakraborty, Rijuparna; Chowdhury, Subhajit Dutta; Chakraborty, Ajoy Kumar

2018-06-01

In this paper, we report the results of our theoretical studies on the phenomenon of self-imaging of periodic object under the illumination of zero-order Bessel beam. Our theoretical analysis indicates that the self-images are visible only after the walk-off distance of the Bessel beam used. It is also observed that the self-images bend around the optical axis of the setup. Besides, the present study justifies the importance of the conditions stipulated by Montgomery.

Practical realization of a microwave Bessel beam launcher

KAUST Repository

Manzhura, Oksana

2011-08-01

An experimental setup is realized to practically generate Bessel beams in the microwave regime. The setup, which consists of a series of circular loop antennas inserted coaxially inside a circular metallic waveguide, excites the waveguide\\'s transverse-electric modes such that their superposition forms a Bessel beam at the open-end of the waveguide. The excitation currents are calculated from the needed excitation coefficients of each guided mode, which, in turn, are calculated from the modal decomposition of the beam. The efficiency of the setup is evaluated and the obtained experimental results are compared to the theoretical estimates. © 2011 IEEE.

On the validity of localized approximation for an on-axis zeroth-order Bessel beam

International Nuclear Information System (INIS)

Gouesbet, Gérard; Lock, J.A.; Ambrosio, L.A.; Wang, J.J.

2017-01-01

Localized approximation procedures are efficient ways to evaluate beam shape coefficients of laser beams, and are particularly useful when other methods are ineffective or inefficient. Several papers in the literature have reported the use of such procedures to evaluate the beam shape coefficients of Bessel beams. Examining the specific case of an on-axis zeroth-order Bessel beam, we demonstrate that localized approximation procedures are valid only for small axicon angles. - Highlights: • The localized approximation has been widely used to evaluate the Beam Shape Coefficients (BSCs) of Bessel beams. • The validity of this approximation is examined in the case of an on-axis zeroth-order Bessel beam. • It is demonstrated, in this specific example, that the localized approximation is efficient only for small enough axicon angles. • It is easily argued that this result must remain true for any kind of Bessel beams.

Multipole expansion of acoustical Bessel beams with arbitrary order and location.

Science.gov (United States)

Gong, Zhixiong; Marston, Philip L; Li, Wei; Chai, Yingbin

2017-06-01

An exact solution of expansion coefficients for a T-matrix method interacting with acoustic scattering of arbitrary order Bessel beams from an obstacle of arbitrary location is derived analytically. Because of the failure of the addition theorem for spherical harmonics for expansion coefficients of helicoidal Bessel beams, an addition theorem for cylindrical Bessel functions is introduced. Meanwhile, an analytical expression for the integral of products including Bessel and associated Legendre functions is applied to eliminate the integration over the polar angle. Note that this multipole expansion may also benefit other scattering methods and expansions of incident waves, for instance, partial-wave series solutions.

Bessel beam fluorescence lifetime tomography of live embryos (Conference Presentation)

Science.gov (United States)

Xu, Dongli; Peng, Leilei

2016-03-01

Optical tomography allows isotropic 3D imaging of embryos. Scanning-laser optical tomography (SLOT) has superior light collecting efficiency than wide-field optical tomography, making it ideal for fluorescence imaging of live embryos. We previously reported an imaging system that combines SLOT with a novel Fourier-multiplexed fluorescence lifetime imaging (FmFLIM) technique named FmFLIM-SLOT. FmFLIM-SLOT performs multiplexed FLIM-FRET readout of multiple FRET sensors in live embryos. Here we report a recent effort on improving the spatial resolution of the FmFLIM-SLOT system in order to image complex biochemical processes in live embryos at the cellular level. Optical tomography has to compromise between resolution and the depth of view. In SLOT, the commonly-used focused Gaussian beam diverges quickly from the focal plane, making it impossible to achieve high resolution imaging in a large volume specimen. We thus introduce Bessel beam laser-scanning tomography, which illuminates the sample with a spatial-light-modulator-generated Bessel beam that has an extended focal depth. The Bessel beam is scanned across the whole specimen. Fluorescence projection images are acquired at equal angular intervals as the sample rotates. Reconstruction artifacts due to annular-rings of the Bessel beam are removed by a modified 3D filtered back projection algorithm. Furthermore, in combination of Fourier-multiplexing fluorescence lifetime imaging (FmFLIM) method, the Bessel FmFLIM-SLOT system is capable of perform 3D lifetime imaging of live embryos at cellular resolution. The system is applied to in-vivo imaging of transgenic Zebrafish embryos. Results prove that Bessel FmFLIM-SLOT is a promising imaging method in development biology research.

Optical breakdown of helium in Bessel laser radiation beams

International Nuclear Information System (INIS)

Andreev, N E; Pleshanov, I V; Margolin, L Ya; Pyatnitskii, Lev N

1998-01-01

Numerical simulation is used to investigate the dynamics of formation of a helium plasma in Bessel beams, shaped by an axicon and a phase converter from a laser radiation pulse with Gaussian temporal and radial intensity profiles. The beam intensities at the breakdown threshold are determined as a function of the pulse duration for various radial field distributions in a beam characterised by Bessel functions of order m (m = 0 - 5). It is shown that in the investigated range of parameters the threshold intensity is independent of m. The temporal and spatial evolution of the resultant plasma, and the dependence of the plasma characteristics on the pulse parameters are considered. Conditions are found for the formation of tubular plasma channels in beams of orders m≥1. The adopted model of the optical breakdown of helium is shown to be satisfactory because of a good agreement between the results of calculations of the moment of breakdown in a zeroth-order Bessel beam and experimental results. (interaction of laser radiation with matter. laser plasma)

Azimuthally matched interactions and azimuthal correlation of Bessel light beams

International Nuclear Information System (INIS)

Khilo, N A

2000-01-01

A theoretical investigation is reported of the regime of azimuthally matched interactions in the process of conversion of the frequency of Bessel light beams. It is shown that this nonlinear interaction regime is accompanied by the establishment of correlations of the mutual azimuthal orientations of plane-wave components of Bessel beams and by an increase in the overlap integral. (nonlinear optical phenomena)

Expansion of a zero-order Bessel beam in spheroidal coordinates by generalized Lorenz–Mie theory

International Nuclear Information System (INIS)

Han, L.; Han, Y.P.; Cui, Z.W.; Wang, J.J.

2014-01-01

An analytic solution to the scattering of the zero-order Bessel beam by a spheroidal particle is constructed on the basis of the generalized Lorenz–Mie theory (GLMT). The spheroidal beam shape coefficients (BSCs) of the zero-order Bessel beam are directly expressed in spheroidal coordinates and computed conveniently using an intrinsic method. Utilizing the tangential continuity of the electromagnetic fields, the expression coefficients of scattered and internal fields are determined. Numerical results concerning scattered field in the far zone are displayed for various parameters of the incident electromagnetic beam and of the scatter. These results are expected to provide useful insights into the scattering of a Bessel beam by spheroidal particles and particle manipulation applications using Bessel beams. - Highlights: • The scattering of zero-order Bessel beam by dielectric spheroid is investigated. • The analytic solution is constructed within the framework of the GLMT. • The spheroidal beam shape coefficients of the zero-order Bessel beam are computed by use an intrinsic method. • Numerical results concerning scattered field are displayed for various parameters

Analytical study on the self-healing property of Bessel beam

Science.gov (United States)

Chu, X.

2012-10-01

With the help of Babinet principle, an analytical expression for the self-healing of Bessel beam is derived by using the Gaussian absorption function to describe the obstacle. Based on the analytical expression, the self-healing properties of Bessel beam are studied. It shows that Bessel beam has the ability to reconstruct its beam shape disturbed by an obstacle. However, during the self-healing process, not only the intensity of the beam behind the obstacle but also the other part will be affected by the obstruction. Meanwhile, the highlight spot, which intensity is larger than that without the obstacle will appear, and the size and strength of the highlight spot is determined by the size of the obstacle. From the change of Poynting vector and Babinet principle, the physical interpretations for the self-healing ability, the effects of the obstruction on the other part and the appearance of highlight spot are given.

Generation of the second harmonics of Bessel light beams in a KTP crystal

International Nuclear Information System (INIS)

Belyi, V N; Kazak, N S; Kondratyuk, N V; Khilo, N A; Shagov, A A

1998-01-01

Theoretical and experimental investigations were made of the characteristic features of doubling the frequency of Bessel light beams by the oe - e interaction in a KTP crystal. All possible and scalar interactions of plane-wave components of Bessel beams were observed experimentally. The spatial structure of the second harmonic in the far zone consisted of a central spot and a concentric ring. The diffraction divergence of the central beam was weak ( ∼ 1.7 mrad). The energy conversion efficiency was ∼ 21% for a Bessel beam, which was three times higher than the efficiency of conversion of the initial laser beam. A theoretical model was based on representation of the field of the second harmonic as a superposition of Bessel beams, which provided a correct description of the observed spatial and energy characteristics of the second harmonic. (nonlinear optical phenomena and devices)

Controlled acceleration of superimposed Bessel beams

CSIR Research Space (South Africa)

Dudley, Angela L

2013-06-01

Full Text Available spatial light modulator (SLM) to create superimposed, non-canonical, higher-order Bessel beams and a CCD camera to investigate the propagation of the resulting field. It is already known that the intensity profile of the resulting field experiences...

Extension of filament propagation in water with Bessel-Gaussian beams

Energy Technology Data Exchange (ETDEWEB)

Kaya, G.; Sayrac, M.; Boran, Y.; Kolomenskii, A. A. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Kaya, N.; Schuessler, H. A. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Science and Petroleum, Texas A& M University at Qatar, Doha 23874 (Qatar); Strohaber, J. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Department of Physics, Florida A& M University, Tallahassee, Florida 32307 (United States); Amani, M. [Science and Petroleum, Texas A& M University at Qatar, Doha 23874 (Qatar)

2016-03-15

We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.

Electromagnetic scattering by a uniaxial anisotropic sphere located in an off-axis Bessel beam.

Science.gov (United States)

Qu, Tan; Wu, Zhen-Sen; Shang, Qing-Chao; Li, Zheng-Jun; Bai, Lu

2013-08-01

Electromagnetic scattering of a zero-order Bessel beam by an anisotropic spherical particle in the off-axis configuration is investigated. Based on the spherical vector wave functions, the expansion expression of the zero-order Bessel beam is derived, and its convergence is numerically discussed in detail. Utilizing the tangential continuity of the electromagnetic fields, the expressions of scattering coefficients are given. The effects of the conical angle of the wave vector components of the zero-order Bessel beam, the ratio of the radius of the sphere to the central spot radius of the zero-order Bessel beam, the shift of the beam waist center position along both the x and y axes, the permittivity and permeability tensor elements, and the loss of the sphere on the radar cross section (RCS) are numerically analyzed. It is revealed that the maximum RCS appears in the conical direction or neighboring direction when the sphere is illuminated by a zero-order Bessel beam. Furthermore, the RCS will decrease and the symmetry is broken with the shift of the beam waist center.

Theory of third-harmonic generation using Bessel beams, and self-phase-matching

International Nuclear Information System (INIS)

Tewari, S.P.; Huang, H.; Boyd, R.W.

1996-01-01

Taking Bessel beams (J 0 beam) as a representation of a conical beam, and a slowly varying envelope approximation (SVEA) we obtain the results for the theory of third-harmonic generation from an atomic medium. We demonstrate how the phenomenon of self-phase-matching is contained in the transverse-phase-matching integral of the theory. A method to calculate the transverse-phase-matching integral containing four Bessel functions is described which avoids the computer calculations of the Bessel functions. In order to consolidate the SVEA result an alternate method is used to obtain the exact result for the third-harmonic generation. The conditions are identified in which the exact result goes over to the result of the SVEA. The theory for multiple Bessel beams is also discussed which has been shown to be the source of the wide width of the efficiency curve of the third-harmonic generation observed in experiments. copyright 1996 The American Physical Society

Transverse characterization of focused Bessel beams with angular momentum applied to study degree of coherence

International Nuclear Information System (INIS)

He, Xi; Wu, Fengtie; Chen, Ziyang; Pu, Jixiong; Chavez-Cerda, Sabino

2016-01-01

The transverse focusing properties at the ‘pseudo-focal’ plane of coherent Bessel beams with angular momentum are analyzed in detail. The transverse magnification of the central dark region of Bessel beams at this pseudo-focal plane is derived for the first time by calculating the ratio of the magnitude of the transverse components of the corresponding wave vectors before and after the focusing lens. We test our results experimentally with coherent laser Bessel beams and excellent agreement is observed. Then, an LED light source is used to generate Bessel beams. By modifying the coherence of the LED light source, we observe that by reducing coherence a smaller and shallower central dark region of Bessel beams with angular momentum is produced at the pseudo-focal plane. This technique can be used as a method to characterize the degree of coherence of vortex beams. (paper)

Optimal condition for employing an axicon-generated Bessel beam to fabricate cylindrical microlens arrays

Science.gov (United States)

Luo, Zhi; Yin, Kai; Dong, Xinran; Duan, Ji’an

2018-05-01

A numerical algorithm, modelling the transformation from a Gaussian beam to a Bessel beam, is presented for the purpose to study the optimal condition for employing an axicon-generated Bessel beam to fabricate cylindrical microlens arrays (CMLAs). By applying the numerical algorithm to simulate the spatial intensity distribution behind the axicon under different defects of a rotund-apex and different diameter ratios of an incident beam to the axicon, we find that the diffraction effects formed by the axicon edge can be almost eliminated when the diameter ratio is less than 1:2, but the spatial intensity distribution is disturbed dramatically even a few tens of microns deviation of the apex, especially for the front part of the axicon-generated Bessel beam. Fortunately, the lateral intensity profile in the rear part still maintains a desirable Bessel curve. Therefore, the rear part of the Bessel area and the less than 1:2 diameter ratio are the optimal choice for employing an axicon-generated Bessel beam to implement surface microstructures fabrication. Furthermore, by applying the optimal conditions to direct writing microstructures on fused silica with a femtosecond (fs) laser, a large area close-packed CMLA is fabricated. The CMLA presents high quality and uniformity and its optical performance is also demonstrated.

Extension of filament propagation in water with Bessel-Gaussian beams

Directory of Open Access Journals (Sweden)

G. Kaya

2016-03-01

Full Text Available We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.

High-power Bessel beams with orbital angular momentum in the terahertz range

Science.gov (United States)

Choporova, Yu. Yu.; Knyazev, B. A.; Kulipanov, G. N.; Pavelyev, V. S.; Scheglov, M. A.; Vinokurov, N. A.; Volodkin, B. O.; Zhabin, V. N.

2017-08-01

In this paper, we have performed experimental, analytical, and numerical studies of beams with topological charges of ±1 and ±2 formed by silicon binary phase axicons (BPAs) with spiral zone structures. The axicons were illuminated with the Novosibirsk free electron laser radiation (a continuous stream of 100-ps pulses at f =5.6 MHz). The cw power of the beams produced reached 30 W and can by doubled via antireflection coating of the axicons. The intensity distribution in the beam cross sections was in good agreement with the Bessel functions and was kept constant within a distance of about L /r ≈190 and 100, where the first ring radii of the beams r were 0.9 and 1.5 mm for the Bessel beams of the first and second orders, respectively. Although the characteristics of the beams (Bessel cross section, "diffraction-free" propagation, self-recovery after passing obstacles, and randomly inhomogeneous media) corresponded to the properties of ideal Bessel beams, their spatial Fourier spectrum (the image in the focal plane of the lens) was, instead of an ideal ring, intertwined segments of arcs with phases shifted by π , the number of which was equal to the double value of the topological charge. This feature can be used, for example, in a demultiplexing unit of a free vortex-wave communication system or for identification of beam topological charge. We also revisited Young's double-slit diffraction and rotation of beams obstructed by a half-plane, previously applied to Laguerre-Gaussian beam characterization, in the case of the Bessel beams. The Young diffraction pattern demonstrated in this case a complicated intensity-phase distribution. It was shown that the Bessel beams formed by BPAs have two important advantages, which can be used in applications, in comparison with other methods of generation, e.g., a combination of an axicon lens with a spiral phase plate. Although the phase jumps of the axicons are designed for a determined wavelength (141 μ m in our case

Polarization properties of linearly polarized parabolic scaling Bessel beams

Energy Technology Data Exchange (ETDEWEB)

Guo, Mengwen; Zhao, Daomu, E-mail: zhaodaomu@yahoo.com

2016-10-07

The intensity profiles for the dominant polarization, cross polarization, and longitudinal components of modified parabolic scaling Bessel beams with linear polarization are investigated theoretically. The transverse intensity distributions of the three electric components are intimately connected to the topological charge. In particular, the intensity patterns of the cross polarization and longitudinal components near the apodization plane reflect the sign of the topological charge. - Highlights: • We investigated the polarization properties of modified parabolic scaling Bessel beams with linear polarization. • We studied the evolution of transverse intensity profiles for the three components of these beams. • The intensity patterns of the cross polarization and longitudinal components can reflect the sign of the topological charge.

Two-photon polymerization of cylinder microstructures by femtosecond Bessel beams

Energy Technology Data Exchange (ETDEWEB)

Yang, Liang [Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026 (China); Laser Zentrum Hannover e.V., 30419 Hannover (Germany); El-Tamer, Ayman; Hinze, Ulf; Chichkov, Boris N [Laser Zentrum Hannover e.V., 30419 Hannover (Germany); Li, Jiawen, E-mail: jwl@ustc.edu.cn; Hu, Yanlei; Huang, Wenhao; Chu, Jiaru [Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026 (China)

2014-07-28

In this work, we present an approach to modulate femtosecond laser beams into Bessel beams with a spatial light modulator (SLM) for two-photon polymerization applications. Bessel beams with different parameters are generated and annular optical fields are produced at the focal plane of the objective. Uniform cylinder microstructures are fabricated by a single illumination during a few seconds without stage translation. By modulating the holograms encoded on the SLM, the diameters of the fabricated annular structures can be flexibly controlled in a wide range with no need of changing the optical elements and realignment of the optical path.

THz computed tomography system with zero-order Bessel beam

Science.gov (United States)

Niu, Liting; Wu, Qiao; Wang, Kejia; Liu, Jinsong; Yang, Zhengang

2018-01-01

Terahertz (THz) waves can penetrate many optically opaque dielectric materials such as plastics, ceramics and colorants. It is effective to reveal the internal structures of these materials. We have built a THz Computed Tomography (CT) system with 0.3 THz zero-order Bessel beam to improve the depth of focus of this imaging system for the non-diffraction property of Bessel beam. The THz CT system has been used to detect a paper cup with a metal rod inside. Finally, the acquired projection data have been processed by the filtered back-projection algorithm and the reconstructed image of the sample has been obtained.

Photorefractive Axicon: Study of Light-induced Effect by Bessel Beam in Photorefractive Crystal

International Nuclear Information System (INIS)

Vieira, T A; Gesualdi, M R R; Zamboni-Rached, M; Muramatsu, M

2011-01-01

In this work, we present the theoretical and computational study of the original analysis of the light-induced effects by Bessel beams in photorefractive crystals. Modern applications of these beams as: metrological, alignment of optical systems, optical tweezers, non linear optics, optical communication, and others, becoming a very interesting substitute for a Gaussian beam when this is subject to diffraction and dispersion effects to large distance propagation. On the other hand, the photorefractive crystals are very important materials for applications in non-linear optics, holographic storage, interferometry and optical information processing. We perform an analysis of the index refraction modulation generated by Bessel beam in photorefractive medium discussing the possibility this optical material to control and generation of Bessel beam properties.

Probing the longitudinal electric field of Bessel beams using second-harmonic generation from nano-objects

Science.gov (United States)

Turquet, Léo; Kakko, Joona-Pekko; Karvonen, Lasse; Jiang, Hua; Kauppinen, Esko; Lipsanen, Harri; Kauranen, Martti; Bautista, Godofredo

2017-08-01

Non-diffractive Bessel beams are receiving significant interest in optical microscopy due to their remarkably large depth of field. For example, studies have shown the superiority of Bessel beams over Gaussian beams for volumetric imaging of three-dimensionally thick or extended samples. However, the vectorial aspects of the focal fields of Bessel beams are generally obscured when traditional methods are used to characterize their three-dimensional point-spread function in space, which contains contributions from all optical field components. Here, we show experimentally the three-dimensional spatial distribution and enhanced depth of field of the longitudinal electric field components of a focused linearly-polarized Bessel beam. This is done through second-harmonic generation from well-defined vertically-aligned gallium-arsenide nanowires, whose second-order response is primarily driven by the longitudinal fields at the beam focus.

Optical pulling force on a magneto-dielectric Rayleigh sphere in Bessel tractor polarized beams

International Nuclear Information System (INIS)

Mitri, F.G.; Li, R.X.; Yang, R.P.; Guo, L.X.; Ding, C.Y.

2016-01-01

The optical radiation force induced by Bessel (vortex) beams on a magneto-dielectric subwavelength sphere is investigated with particular emphasis on the beam polarization and order l (or topological charge). The analysis is focused on identifying the regions and some of the conditions to achieve retrograde motion of the sphere centered on the axis of wave propagation of the incident beam, or shifted off-axially. Exact non-paraxial analytical solutions are established, and computations for linear, circular, radial, azimuthal and mixed polarizations of the individual plane wave components forming the Bessel (vortex) beams by means of the angular spectrum decomposition method (ASDM) illustrate the theory with particular emphasis on the tractor (i.e. reversal) behavior of the force. This effect results in the pulling of the magneto-dielectric sphere against the forward linear momentum density flux associated with the incoming waves. Should some conditions related to the choice of the beam parameters as well as the permittivity and permeability of the sphere be met, the optical force vanishes and reverses sign. Moreover, the beam polarization is shown to affect differently the axial negative pulling force for either the zeroth- or the first-order Bessel beam. When the sphere is centered on the beam′s axis, the axial force component is always negative for the zeroth-order Bessel beam except for the radial and azimuthal polarization configurations. Nonetheless, for the first-order Bessel beam, the axial force is negative for the radial polarization case only. Additional tractor beam effects arise when the sphere departs from the center of the beam. It is also demonstrated that the tractor beam effect arises from the force component originating from the cross-interaction between the electric and magnetic dipoles. Potential applications are in particle manipulation, optical levitation, tractor beam tweezers, and other emergent technologies using polarized Bessel beams on

Orbital angular momentum of a high-order Bessel light beam

International Nuclear Information System (INIS)

Volke-Sepulveda, K; Garces-Chavez, V; Chavez-Cerda, S; Arlt, J; Dholakia, K

2002-01-01

The orbital angular momentum density of Bessel beams is calculated explicitly within a rigorous vectorial treatment. This allows us to investigate some aspects that have not been analysed previously, such as the angular momentum content of azimuthally and radially polarized beams. Furthermore, we demonstrate experimentally the mechanical transfer of orbital angular momentum to trapped particles in optical tweezers using a high-order Bessel beam. We set transparent particles of known dimensions into rotation, where the sense of rotation can be reversed by changing the sign of the singularity. Quantitative results are obtained for rotation rates. This paper's animations are available from the Multimedia Enhancements page

Effective and efficient method of calculating Bessel beam fields

CSIR Research Space (South Africa)

Litvin, IA

2005-01-01

Full Text Available Bessel beams have gathered much interest of late due to their properties of near diffraction free propagation and self reconstruction after obstacles. Such laser beams have already found applications in fields such as optical tweezers and as pump...

Propagation of high-order circularly polarized Bessel beams and vortex generation in uniaxial crystals

CSIR Research Space (South Africa)

Belyi, VN

2011-05-01

Full Text Available The authors investigate the generation and transformation of Bessel beams through linear and nonlinear optical crystals. They outline the generation of high-order vortices due to propagation of Bessel beams along the optical axis of uniaxial...

Spin polarisation with electron Bessel beams

Energy Technology Data Exchange (ETDEWEB)

Schattschneider, P., E-mail: schattschneider@ifp.tuwien.ac.at [Institut für Festkörperphysik, Technische Universität Wien, A-1040 Wien (Austria); USTEM, Technische Universität Wien, A-1040 Wien (Austria); Grillo, V. [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); CNR-IMEM, Parco delle Scienze 37a, I-43100 Parma (Italy); Aubry, D. [Centrale Supelec, MSSMast CNRS 8579, F-92295 Châtenay-Malabry (France)

2017-05-15

The theoretical possibility to use an electron microscope as a spin polarizer is studied. It turns out that a Bessel beam passing a standard magnetic objective lens is intrinsically spin polarized when post-selected on-axis. In the limit of infinitely small detectors, the spin polarisation tends to 100 %. Increasing the detector size, the polarisation decreases rapidly, dropping below 10{sup −4} for standard settings of medium voltage microscopes. For extremely low voltages, the Figure of Merit increases by two orders of magnitude, approaching that of existing Mott detectors. Our findings may lead to new desings of spin filters, an attractive option in view of its inherent combination with the electron microscope, especially at low voltage. - Highlights: • TEM round magnetic lenses can act as spin polarizers when a Bessel beam is sent through. • This is found on theoretical grounds and demonstrated numerically for a few cases. • The effect is small, but can reach a Figure of Merit similar to existing Mott detectors. • This opens the possibility to construct nanometer-sized spin filters or detectors.

Bessel beam CARS of axially structured samples

Science.gov (United States)

Heuke, Sandro; Zheng, Juanjuan; Akimov, Denis; Heintzmann, Rainer; Schmitt, Michael; Popp, Jürgen

2015-06-01

We report about a Bessel beam CARS approach for axial profiling of multi-layer structures. This study presents an experimental implementation for the generation of CARS by Bessel beam excitation using only passive optical elements. Furthermore, an analytical expression is provided describing the generated anti-Stokes field by a homogeneous sample. Based on the concept of coherent transfer functions, the underling resolving power of axially structured geometries is investigated. It is found that through the non-linearity of the CARS process in combination with the folded illumination geometry continuous phase-matching is achieved starting from homogeneous samples up to spatial sample frequencies at twice of the pumping electric field wave. The experimental and analytical findings are modeled by the implementation of the Debye Integral and scalar Green function approach. Finally, the goal of reconstructing an axially layered sample is demonstrated on the basis of the numerically simulated modulus and phase of the anti-Stokes far-field radiation pattern.

Spatial characterization of Bessel-like beams for strong-field physics.

Science.gov (United States)

Summers, Adam M; Yu, Xiaoming; Wang, Xinya; Raoul, Maxime; Nelson, Josh; Todd, Daniel; Zigo, Stefan; Lei, Shuting; Trallero-Herrero, Carlos A

2017-02-06

We present a compact, simple design for the generation and tuning of both the spot size and effective focal length of Bessel-like beams. In particular, this setup provides an important tool for the use of Bessel-like beams with high-power, femtosecond laser systems. Using a shallow angle axicon in conjunction with a spherical lens, we show that it is possible to focus Bessel-like modes to comparable focal spot sizes to sharp axicons while maintaining a long effective focal length. The resulting focal profiles are characterized in detail using an accurate high dynamic range imaging technique. Quantitatively, we introduce a metric (R0.8) which defines the spot-size containing 80% of the total energy. Our setup overcomes the typical compromise between long working distances and small spot sizes. This is particularly relevant for strong-field physics where most experiments must operate in vacuum.

Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio

Science.gov (United States)

Gong, Zhixiong; Li, Wei; Mitri, Farid G.; Chai, Yingbin; Zhao, Yao

2016-11-01

In this paper, the T-matrix (null-field) method is applied to investigate the acoustic scattering by a large-aspect-ratio rigid spheroid immersed in a non-viscous fluid under the illumination of an unbounded zeroth-order Bessel beam with arbitrary orientation. Based on the proposed method, a MATLAB software package is constructed accordingly, and then verified and validated to compute the acoustic scattering by a rigid oblate or prolate spheroid in the Bessel beam. Several numerical examples are carried out to investigate the novel phenomenon of acoustic scattering by spheroids in Bessel beams with arbitrary incidence, with particular emphasis on the aspect ratio (i.e. the ratio of the polar radius over the equatorial radius of the spheroid), the half-cone angle of Bessel beam, the dimensionless frequency, as well as the angle of incidence. The quasi-periodic oscillations are observed in the plots of the far-field backscattering form function modulus versus the dimensionless frequency, owing to the interference between the specular reflection and the Franz wave circumnavigating the spheroid in the surrounding fluid. Furthermore, the 3D far-field scattering directivity patterns at end-on incidence and 2D polar plots at arbitrary angles of incidence are exhibited, which could provide new insights into the physical mechanisms of Bessel beam scattering by flat or elongated spheroid. This research work may provide an impetus for the application of acoustic Bessel beam in engineering practices.

Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams

CSIR Research Space (South Africa)

Milione, G

2015-02-01

Full Text Available be simply understood via geometric optics [3]. When a portion of a Bessel beam is obstructed in one plane, the unobstructed conical rays interfere in its shadow region in another plane, as shown in Fig. 1(e). Due to this property, Bessel beams have been... extensively studied and have been used for a number of applications; for comprehensive reviews see [4–7]. For example, when using a Bessel beam for optical trapping, it is possible to simultaneously trap multiple particles in well separated planes [8...

Light scattering of a Bessel beam by a nucleated biological cell: An eccentric sphere model

Science.gov (United States)

Wang, Jia Jie; Han, Yi Ping; Chang, Jiao Yong; Chen, Zhu Yang

2018-02-01

Within the framework of generalized Lorenz-Mie theory (GLMT), an eccentrically stratified dielectric sphere model illuminated by an arbitrarily incident Bessel beam is applied to investigate the scattering characteristics of a single nucleated biological cell. The Bessel beam propagating in an arbitrary direction is expanded in terms of vector spherical wave functions (VSWFs), where the beam shape coefficients (BSCs) are calculated rigorously in a closed analytical form. The effects of the half-cone angle of Bessel beam, the location of the particle in the beam, the size ratio of nucleus to cell, and the location of the nucleus inside the cell on the scattering properties of a nucleated cell are analyzed. The results provide useful references for optical diagnostic and imaging of particle having nucleated structure.

Rapid volumetric imaging with Bessel-Beam three-photon microscopy

Science.gov (United States)

Chen, Bingying; Huang, Xiaoshuai; Gou, Dongzhou; Zeng, Jianzhi; Chen, Guoqing; Pang, Meijun; Hu, Yanhui; Zhao, Zhe; Zhang, Yunfeng; Zhou, Zhuan; Wu, Haitao; Cheng, Heping; Zhang, Zhigang; Xu, Chris; Li, Yulong; Chen, Liangyi; Wang, Aimin

2018-01-01

Owing to its tissue-penetration ability, multi-photon fluorescence microscopy allows for the high-resolution, non-invasive imaging of deep tissue in vivo; the recently developed three-photon microscopy (3PM) has extended the depth of high-resolution, non-invasive functional imaging of mouse brains to beyond 1.0 mm. However, the low repetition rate of femtosecond lasers that are normally used in 3PM limits the temporal resolution of point-scanning three-photon microscopy. To increase the volumetric imaging speed of 3PM, we propose a combination of an axially elongated needle-like Bessel-beam with three-photon excitation (3PE) to image biological samples with an extended depth of focus. We demonstrate the higher signal-to-background ratio (SBR) of the Bessel-beam 3PM compared to the two-photon version both theoretically and experimentally. Finally, we perform simultaneous calcium imaging of brain regions at different axial locations in live fruit flies and rapid volumetric imaging of neuronal structures in live mouse brains. These results highlight the unique advantage of conducting rapid volumetric imaging with a high SBR in the deep brain in vivo using scanning Bessel-3PM.

Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series

International Nuclear Information System (INIS)

Li, Renxian; Ren, Kuan Fang; Han, Xiang'e; Wu, Zhensen; Guo, Lixin; Gong, Shuxi

2013-01-01

Debye series expansion (DSE) is employed to the analysis of radiation pressure force (RPF) exerted on biological cells induced by high-order Bessel beams (BB). The beam shape coefficients (BSCs) for high-order Bessel beams are calculated using analytical expressions obtained by the integral localized approximation (ILA). Different types of cells, including a real Chinese Hamster Ovary (CHO) cell and a lymphocyte which are respectively modeled by a coated and five-layered sphere, are considered. The RPF induced by high-order Bessel beams is compared with that by Gaussian beams and zeroth-order Bessel beams, and the effect of different scattering processes on RPF is studied. Numerical calculations show that high-order Bessel beams with zero central intensity can also transversely trap particle in the beam center, and some scattering processes can provide longitudinal pulling force. -- Highlights: ► BSCs for high-order Bessel beam (HOBB) is derived using ILA. ► DSE is employed to study the RPF induced by HOBB exerted on multilayered cells. ► RPF is decided by radius relative to the interval of peaks in intensity profile. ► HOBB can also transversely trap high-index particle in the vicinity of beam axis. ► RPF for some scattering processes can longitudinally pull particles back

Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers

International Nuclear Information System (INIS)

Mitri, F.G.

2008-01-01

Starting from the exact acoustic scattering from a sphere immersed in an ideal fluid and centered along the propagation axis of a standing or quasi-standing zero-order Bessel beam, explicit partial-wave representations for the radiation force are derived. A standing or a quasi-standing acoustic field is the result of propagating two equal or unequal amplitude zero-order Bessel beams, respectively, along the same axis but in opposite sense. The Bessel beam is characterized by the half-cone angle β of its plane wave components, such that β = 0 represents a plane wave. It is assumed here that the half-cone angle β for each of the counter-propagating acoustic Bessel beams is equal. Fluid, elastic and viscoelastic spheres immersed in water are treated as examples. Results indicate the capability of manipulating spherical targets based on their mechanical and acoustical properties. This condition provides an impetus for further designing acoustic tweezers operating with standing or quasi-standing Bessel acoustic waves. Potential applications include particle manipulation in micro-fluidic lab-on-chips as well as in reduced gravity environments

Creation of matter wave Bessel beams and observation of quantized circulation in a Bose–Einstein condensate

International Nuclear Information System (INIS)

Ryu, C; Henderson, K C; Boshier, M G

2014-01-01

Bessel beams are plane waves with amplitude profiles described by Bessel functions. They are important because they propagate ‘diffraction-free’ and because they can carry orbital angular momentum. Here we report the creation of a Bessel beam of de Broglie matter waves. The Bessel beam is produced by the free evolution of a thin toroidal atomic Bose–Einstein condensate (BEC) which has been set into rotational motion. By attempting to stir it at different rotation rates, we show that the toroidal BEC can only be made to rotate at discrete, equally spaced frequencies, demonstrating that circulation is quantized in atomic BECs. The method used here can be viewed as a form of wavefunction engineering which might be developed to implement cold atom matter wave holography. (paper)

Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid

Science.gov (United States)

Mitri, F. G.

2015-12-01

Partial-wave series representation of the acoustic scattering field of high-order Bessel vortex beams by rigid oblate and prolate spheroids using the modal matching method is developed. The method, which is applicable to slightly elongated objects at low-to-moderate frequencies, requires solving a system of linear equations which depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated partial-wave series expansions (PWSEs), and satisfying the Neumann boundary condition for a rigid immovable surface in the least-squares sense. This original semi-analytical approach developed for Bessel vortex beams is demonstrated for finite oblate and prolate spheroids, where the mathematical functions describing the spheroidal geometry are written in a form involving single angular (polar) integrals that are numerically computed. The transverse (θ = π / 2) and 3D scattering directivity patterns are evaluated in the far-field for both prolate and oblate spheroids, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid) not exceeding 3:1, the half-cone angle β and order m of the Bessel vortex beam, as well as the dimensionless size parameter kr0. Periodic oscillations in the magnitude plots of the far-field scattering form function are observed, which result from the interference of the reflected waves with the circumferential (Franz') waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3D directivity patterns illustrate the far-field scattering from the spheroid, that vanishes in the forward (θ = 0) and backward (θ = π) directions. Particular applications in underwater acoustics and scattering, acoustic levitation and the detection of submerged elongated objects using Bessel vortex waves to name a few, would benefit from the results of the present investigation.

Particle confinement by a radially polarized laser Bessel beam

Science.gov (United States)

Laredo, Gilad; Kimura, Wayne D.; Schächter, Levi

2017-03-01

The stable trajectory of a charged particle in an external guiding field is an essential condition for its acceleration or for forcing it to generate radiation. Examples of possible guiding devices include a solenoidal magnetic field or permanent periodic magnet in klystrons, a wiggler in free-electron lasers, the lattice of any accelerator, and finally the crystal lattice for the case of channeling radiation. We demonstrate that the trajectory of a point-charge in a radially polarized laser Bessel beam may be stable similarly to the case of a positron that bounces back and forth in the potential well generated by two adjacent atomic planes. While in the case of channeling radiation, the transverse motion is controlled by a harmonic oscillator equation, for a Bessel beam the transverse motion is controlled by the Mathieu equation. Some characteristics of the motion are presented.

Generating superpositions of higher order bessel beams [Conference paper

CSIR Research Space (South Africa)

Vasilyeu, R

2009-10-01

Full Text Available An experimental setup to generate a superposition of higher-order Bessel beams by means of a spatial light modulator and ring aperture is presented. The experimentally produced fields are in good agreement with those calculated theoretically....

Terahertz plasmonic Bessel beamformer

International Nuclear Information System (INIS)

Monnai, Yasuaki; Shinoda, Hiroyuki; Jahn, David; Koch, Martin; Withayachumnankul, Withawat

2015-01-01

We experimentally demonstrate terahertz Bessel beamforming based on the concept of plasmonics. The proposed planar structure is made of concentric metallic grooves with a subwavelength spacing that couple to a point source to create tightly confined surface waves or spoof surface plasmon polaritons. Concentric scatterers periodically incorporated at a wavelength scale allow for launching the surface waves into free space to define a Bessel beam. The Bessel beam defined at 0.29 THz has been characterized through terahertz time-domain spectroscopy. This approach is capable of generating Bessel beams with planar structures as opposed to bulky axicon lenses and can be readily integrated with solid-state terahertz sources

Self-healing of Bessel-like beams with longitudinally dependent cone angles

CSIR Research Space (South Africa)

Litvin, I

2015-09-01

Full Text Available non-diffracting propagation region. Here we show that such beams can self-heal. Moreover, in contrast to Bessel beams where the self-healing distance is constant, here the self-healing distance is dependent on where the obstruction is placed...

Nonparaxial Bessel and Bessel-Gauss pincers light-sheets

Science.gov (United States)

Mitri, F. G.

2017-01-01

Nonparaxial optical Bessel and Bessel-Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.

Generating superpositions of higher–order Bessel beams [Journal article

CSIR Research Space (South Africa)

Vasilyeu, R

2009-12-01

Full Text Available The authors report the first experimental generation of the superposition of higher-order Bessel beams, by means of a spatial light modulator (SLM) and a ring slit aperture. They present illuminating a ring slit aperture with light which has...

An optical tweezer in asymmetrical vortex Bessel-Gaussian beams

Energy Technology Data Exchange (ETDEWEB)

Kotlyar, V. V.; Kovalev, A. A., E-mail: alexeysmr@mail.ru; Porfirev, A. P. [Image Processing Systems Institute, 151 Molodogvardeiskaya St., 443001 Samara (Russian Federation); Department of Technical cybernetics, Samara State Aerospace University, Samara 443086 (Russian Federation)

2016-07-14

We study an optical micromanipulation that comprises trapping, rotating, and transporting 5-μm polystyrene microbeads in asymmetric Bessel-Gaussian (BG) laser beams. The beams that carry orbital angular momentum are generated by means of a liquid crystal microdisplay and focused by a microobjective with a numerical aperture of NA = 0.85. We experimentally show that given a constant topological charge, the rate of microparticle motion increases near linearly with increasing asymmetry of the BG beam. Asymmetric BG beams can be used instead of conventional Gaussian beam for trapping and transferring live cells without thermal damage.

Generation of high-order Bessel vortex beam carrying orbital angular momentum using multilayer amplitude-phase-modulated surfaces in radiofrequency domain

Science.gov (United States)

Kou, Na; Yu, Shixing; Li, Long

2017-01-01

A high-order Bessel vortex beam carrying orbital angular momentum (OAM) is generated by using multilayer amplitude-phase-modulated surfaces (APMSs) at 10 GHz. The APMS transmitarray is composed of four-layer conformal square-loop (FCSL) surfaces with both amplitude and phase modulation. The APMS can transform a quasi-spherical wave emitted from the feeding source into a pseudo non-diffractive high-order Bessel vortex beam with OAM. The APMS for a second-order Bessel beam carrying OAM in the n = 2 mode is designed, fabricated, and measured. Full-wave simulation and measurement results confirm that Bessel vortex beams with OAM can be effectively generated using the proposed APMS transmitarray.

Bessel beam transformation in c-cuts of uniaxial crystals by varying the source wavelength

Energy Technology Data Exchange (ETDEWEB)

Paranin, V. D. [Samara State Aerospace University, 34, Moskovskoe shosse, Samara, 443086 (Russian Federation)

2016-04-13

Transformation of Bessel beam of a zero order to Bessel beam of the second order in c-cut of CaCO{sub 3} crystal is experimentally investigated. Possibility of output beam control at changing of wavelength and using of a diffraction axicon is shown. Full transformation of beams at changing of wavelength Δλ=1.5 nanometers is received at initial wavelength λ=637.5 nanometers for a crystal of CaCO{sub 3} with 15 mm long and a diffraction axicon with period of 2 microns. The theoretical value of necessary wavelength changing is Δλ=1.7 nanometers that is according with experimental results.

Resonant Self-Trapping and Absorption of Intense Bessel Beams

International Nuclear Information System (INIS)

Fan, J.; Parra, E.; Milchberg, H. M.

2000-01-01

We report the observation of resonant self-trapping and enhanced laser-plasma heating resulting from propagation of high intensity Bessel beams in neutral gas. The enhancement in absorption and plasma heating is directly correlated to the spatial trapping of laser radiation. (c) 2000 The American Physical Society

Efficient second-harmonic imaging of collagen in histological slides using Bessel beam excitation

Science.gov (United States)

Vuillemin, Nelly; Mahou, Pierre; Débarre, Delphine; Gacoin, Thierry; Tharaux, Pierre-Louis; Schanne-Klein, Marie-Claire; Supatto, Willy; Beaurepaire, Emmanuel

2016-07-01

Second-harmonic generation (SHG) is the most specific label-free indicator of collagen accumulation in widespread pathologies such as fibrosis, and SHG-based measurements hold important potential for biomedical analyses. However, efficient collagen SHG scoring in histological slides is hampered by the limited depth-of-field of usual nonlinear microscopes relying on focused Gaussian beam excitation. In this work we analyze theoretically and experimentally the use of Bessel beam excitation to address this issue. Focused Bessel beams can provide an axially extended excitation volume for nonlinear microscopy while preserving lateral resolution. We show that shaping the focal volume has consequences on signal level and scattering directionality in the case of coherent signals (such as SHG) which significantly differ from the case of incoherent signals (two-photon excited fluorescence, 2PEF). We demonstrate extended-depth SHG-2PEF imaging of fibrotic mouse kidney histological slides. Finally, we show that Bessel beam excitation combined with spatial filtering of the harmonic light in wave vector space can be used to probe collagen accumulation more efficiently than the usual Gaussian excitation scheme. These results open the way to SHG-based histological diagnoses.

Axial and transverse acoustic radiation forces on a fluid sphere placed arbitrarily in Bessel beam standing wave tweezers

International Nuclear Information System (INIS)

Mitri, F.G.

2014-01-01

The axial and transverse radiation forces on a fluid sphere placed arbitrarily in the acoustical field of Bessel beams of standing waves are evaluated. The three-dimensional components of the time-averaged force are expressed in terms of the beam-shape coefficients of the incident field and the scattering coefficients of the fluid sphere using a partial-wave expansion (PWE) method. Examples are chosen for which the standing wave field is composed of either a zero-order (non-vortex) Bessel beam, or a first-order Bessel vortex beam. It is shown here, that both transverse and axial forces can push or pull the fluid sphere to an equilibrium position depending on the chosen size parameter ka (where k is the wave-number and a the sphere’s radius). The corresponding results are of particular importance in biophysical applications for the design of lab-on-chip devices operating with Bessel beams standing wave tweezers. Moreover, potential investigations in acoustic levitation and related applications in particle rotation in a vortex beam may benefit from the results of this study. -- Highlights: •The axial and transverse forces on a fluid sphere in acoustical Bessel beams tweezers are evaluated. •The attraction or repulsion to an equilibrium position in the standing wave field is examined. •Potential applications are in particle manipulation using standing waves

Axial and transverse acoustic radiation forces on a fluid sphere placed arbitrarily in Bessel beam standing wave tweezers

Energy Technology Data Exchange (ETDEWEB)

Mitri, F.G., E-mail: mitri@chevron.com

2014-03-15

The axial and transverse radiation forces on a fluid sphere placed arbitrarily in the acoustical field of Bessel beams of standing waves are evaluated. The three-dimensional components of the time-averaged force are expressed in terms of the beam-shape coefficients of the incident field and the scattering coefficients of the fluid sphere using a partial-wave expansion (PWE) method. Examples are chosen for which the standing wave field is composed of either a zero-order (non-vortex) Bessel beam, or a first-order Bessel vortex beam. It is shown here, that both transverse and axial forces can push or pull the fluid sphere to an equilibrium position depending on the chosen size parameter ka (where k is the wave-number and a the sphere’s radius). The corresponding results are of particular importance in biophysical applications for the design of lab-on-chip devices operating with Bessel beams standing wave tweezers. Moreover, potential investigations in acoustic levitation and related applications in particle rotation in a vortex beam may benefit from the results of this study. -- Highlights: •The axial and transverse forces on a fluid sphere in acoustical Bessel beams tweezers are evaluated. •The attraction or repulsion to an equilibrium position in the standing wave field is examined. •Potential applications are in particle manipulation using standing waves.

Study of graphitic microstructure formation in diamond bulk by pulsed Bessel beam laser writing

Science.gov (United States)

Kumar, S.; Sotillo, B.; Chiappini, A.; Ramponi, R.; Di Trapani, P.; Eaton, S. M.; Jedrkiewicz, O.

2017-11-01

The advantages of using Bessel beams for the generation of graphitic structures in diamond bulk are presented. We show that by irradiating the sample with a pulsed Bessel beam whose non-diffracting zone is of the same order of the sample thickness, it is possible to produce without any sample translation straight graphitic through-microstructures, whose size depends on the input pulse energy. The microstructure growth is investigated as a function of the number of irradiating pulses, and the femtosecond and picosecond regimes are contrasted.

Negative optical spin torque wrench of a non-diffracting non-paraxial fractional Bessel vortex beam

International Nuclear Information System (INIS)

Mitri, F.G.

2016-01-01

An absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque. The axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field. Particular emphasis is given on the polarization as well as changing the topological charge α and the half-cone angle of the beam. When α is zero, the axial spin torque component vanishes. However, when α becomes a real positive number, the vortex beam induces left-handed (negative) axial spin torque as the sphere shifts off-axially from the center of the beam. The results show that a non-diffracting non-paraxial fractional Bessel vortex beam is capable of inducing a spin reversal of an absorptive Rayleigh sphere placed arbitrarily in its path. Potential applications are yet to be explored in particle manipulation, rotation in optical tweezers, optical tractor beams, and the design of optically-engineered metamaterials to name a few areas. - Highlights: • Optical nondiffracting nonparaxial fractional Bessel vortex beam is considered. • Negative spin torque on an absorptive dielectric Rayleigh sphere is predicted numerically. • Negative spin torque occurs as the sphere departs from the center of the beam.

Generating millimeter-wave Bessel beam with orbital angular momentum using reflective-type metasurface inherently integrated with source

Science.gov (United States)

Shen, Yizhu; Yang, Jiawei; Meng, Hongfu; Dou, Wenbin; Hu, Sanming

2018-04-01

Metasurfaces, orbital angular momenta (OAM), and non-diffractive Bessel beams have been attracting worldwide research. Combining the benefits of these three promising techniques, this paper proposes a metasurface-based reflective-type approach to generate a first-order Bessel beam carrying OAM. To validate this approach, a millimeter-wave metasurface is analyzed, designed, fabricated, and measured. Experimental results agree well with simulation. Moreover, this reflective-type metasurface, generating a Bessel beam with OAM, is inherently integrated with a planar feeding source in the same single-layer printed circuit board. Therefore, the proposed design features low profile, low cost, easy integration with front-end active circuits, and no alignment error between the feeding source and the metasurface.

Special features of local spatial spectrum of Bessel light beams

CSIR Research Space (South Africa)

Belyi, VN

2011-11-01

Full Text Available In this paper the authors consider the angular spectrum of an apertured Bessel beam when the aperture is circular and shifted laterally with respect to the optical axis. Since the perturbation of the resulting angular spectrum is due to a spatially...

Radiophotoluminescence of alkali-halide crystals stimulated by Bessel laser beam

CERN Document Server

Lyakh, V V; Kochubey, D I; Gyunsburg, K E; Zvezdova, N P; Kochubey, D I; Sedova, Y G; Koronkevich, V P; Poleschuk, A G; Sedukhin, A G

2000-01-01

A new approach to realization of optimal high-resolution reading of deep X-ray images in X-ray-sensitive materials on the base of alkali-halide crystals modified with admixtures has been suggested and investigated experimentally. A possibility to use diffraction axicons with ring aperture for forming micron bright light beams (spatially truncated Bessel beams) which can efficiently de-excite radiophotoluminescence centers lying at large depth in crystals is also presented.

Ultrafast Bessel beams: advanced tools for laser materials processing

Science.gov (United States)

Stoian, Razvan; Bhuyan, Manoj K.; Zhang, Guodong; Cheng, Guanghua; Meyer, Remy; Courvoisier, Francois

2018-05-01

Ultrafast Bessel beams demonstrate a significant capacity of structuring transparent materials with a high degree of accuracy and exceptional aspect ratio. The ability to localize energy on the nanometer scale (bypassing the 100-nm milestone) makes them ideal tools for advanced laser nanoscale processing on surfaces and in the bulk. This allows to generate and combine micron and nano-sized features into hybrid structures that show novel functionalities. Their high aspect ratio and the accurate location can equally drive an efficient material modification and processing strategy on large dimensions. We review, here, the main concepts of generating and using Bessel non-diffractive beams and their remarkable features, discuss general characteristics of their interaction with matter in ablation and material modification regimes, and advocate their use for obtaining hybrid micro and nanoscale structures in two and three dimensions (2D and 3D) performing complex functions. High-throughput applications are indicated. The example list ranges from surface nanostructuring and laser cutting to ultrafast laser welding and the fabrication of 3D photonic systems embedded in the volume.

Limitations to laser machining of silicon using femtosecond micro-Bessel beams in the infrared

International Nuclear Information System (INIS)

Grojo, David; Mouskeftaras, Alexandros; Delaporte, Philippe; Lei, Shuting

2015-01-01

We produce and characterize high-angle femtosecond Bessel beams at 1300-nm wavelength leading to nonlinearly ionized plasma micro-channels in both glass and silicon. With microjoule pulse energy, we demonstrate controlled through-modifications in 150-μm glass substrates. In silicon, strong two-photon absorption leads to larger damages at the front surface but also a clamping of the intensity inside the bulk at a level of ≈4 × 10 11  W cm −2 which is below the threshold for volume and rear surface modification. We show that the intensity clamping is associated with a strong degradation of the Bessel-like profile. The observations highlight that the inherent limitation to ultrafast energy deposition inside semiconductors with Gaussian focusing [Mouskeftaras et al., Appl. Phys. Lett. 105, 191103 (2014)] applies also for high-angle Bessel beams

Superpositions of higher-order bessel beams and nondiffracting speckle fields

CSIR Research Space (South Africa)

Dudley, Angela L

2009-08-01

Full Text Available speckle fields. The paper reports on illuminating a ring slit aperture with light which has an azimuthal phase dependence, such that the field produced is a superposition of two higher-order Bessel beams. In the case that the phase dependence of the light...

Two-color above-threshold ionization of atoms and ions in XUV Bessel beams and intense laser light

Science.gov (United States)

Seipt, D.; Müller, R. A.; Surzhykov, A.; Fritzsche, S.

2016-11-01

The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultraviolet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target atoms with regard to the beam axis. In addition, analog to the circular dichroism in typical two-color ATI experiments with circularly polarized light, we define and discuss seven different dichroism signals for such vortex Bessel beams that arise from the various combinations of the orbital and spin angular momenta of the two light fields. For localized targets, it is found that these dichroism signals strongly depend on the size and position of the atoms relative to the beam. For macroscopically extended targets, in contrast, three of these dichroism signals tend to zero, while the other four just coincide with the standard circular dichroism, similar as for Bessel beams with a small opening angle. Detailed computations of the dichroism are performed and discussed for the 4 s valence-shell photoionization of Ca+ ions.

Efficient sorting of Bessel beams [Conference paper

CSIR Research Space (South Africa)

Mhlanga, T

2013-02-01

Full Text Available measured in entanglement and shown an increased spiral bandwidth17. Exploiting these properties of Bessel beams will make them very useful in the field of long-range, broad bandwidth communication systems. However, in order for these fields to be a... success in the area of optical communication, efficient techniques for extracting the information they carry (i.e. their azimuthal mode indices) need to exist. The ‘fork’ diffraction grating can be used to couple light of a particular OAM state into a...

Enhancement of photorefractive two wave mixing gain with a Bessel pump beam

International Nuclear Information System (INIS)

Biswas, Dhruba J.; Padma Nilaya, J.; Danailov, Miltcho, B.

2001-07-01

The performance of a photo-refractive amplifier has been shown to greatly improve when a diffraction free beam is employed as the pump source. It has been established experimentally that this behaviour owes primarily to the ability of this beam to propagate in the photo-refractive crystal will less fanning. A qualitative explanation for the reduction of fanning with Bessel beam is offered. (author)

Experimental generation and application of the superposition of higher-order Bessel beams

CSIR Research Space (South Africa)

Dudley, Angela L

2009-07-01

Full Text Available Academy of Sciences of Belarus 4 School of Physics, University of Stellenbosch Presented at the 2009 South African Institute of Physics Annual Conference University of KwaZulu-Natal Durban, South Africa 6-10 July 2009 Page 2 © CSIR 2008... www.csir.co.za Generation of Bessel Fields: • METHOD 1: Ring Slit Aperture • METHOD 2: Axicon Adaptation of method 1 to produce superpositions of higher-order Bessel beams: J. Durnin, J.J. Miceli and J.H. Eberly, Phys. Rev. Lett. 58 1499...

The compact converter of Bessel beams of zero and second orders on the basis of z-cut lithium niobate

International Nuclear Information System (INIS)

Paranin, V D; Karpeev, S V; Khonina, S N; Tukmakov, K N

2016-01-01

Transformation of zero-order Bessel beams into a second-order vortex beam in the process of propagation in a c-cut of lithium niobate LiNbO 3 crystal has been investigated experimentally. The possibility of controlling beam transformation by means of changing the curve radius of the illuminating beam is shown. The possibility of Bessel beam transforming by compact devices on the basis of thin c-cuts of uniaxial crystals with a diffraction mask formed on their surface is proved. (paper)

Negative optical spin torque wrench of a non-diffracting non-paraxial fractional Bessel vortex beam

Science.gov (United States)

Mitri, F. G.

2016-10-01

An absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque. The axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field. Particular emphasis is given on the polarization as well as changing the topological charge α and the half-cone angle of the beam. When α is zero, the axial spin torque component vanishes. However, when α becomes a real positive number, the vortex beam induces left-handed (negative) axial spin torque as the sphere shifts off-axially from the center of the beam. The results show that a non-diffracting non-paraxial fractional Bessel vortex beam is capable of inducing a spin reversal of an absorptive Rayleigh sphere placed arbitrarily in its path. Potential applications are yet to be explored in particle manipulation, rotation in optical tweezers, optical tractor beams, and the design of optically-engineered metamaterials to name a few areas.

Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid.

Science.gov (United States)

Mitri, Farid G

2015-10-01

Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (θ = π) in the near field and the backscattering form function in the far field for both prolate and oblate spheroids are presented and discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle of the Bessel beam, and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) because of the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3-D directivity patterns illustrate the near- and far-field axisymmetric scattering. Investigations in underwater acoustics, particle levitation, scattering, and the detection of submerged elongated objects and other related applications utilizing Bessel waves would benefit from the results of the present study.

Multiple scattering of a zero-order Bessel beam with arbitrary incidence by an aggregate of uniaxial anisotropic spheres

International Nuclear Information System (INIS)

Li, Z.J.; Wu, Z.S.; Qu, T.; Shang, Q.C.; Bai, L.

2016-01-01

Based on the generalized multiparticle Mie theory, multiple scattering of an aggregate of uniaxial anisotropic spheres illuminated by a zero-order Bessel beam (ZOBB) with arbitrary propagation direction is investigated. The particle size and configuration are arbitrary. The arbitrary incident Bessel beam is expanded in terms of spherical vector wave functions (SVWFs). Utilizing the vector addition theorem of SVWFs, interactive and total scattering coefficients are derived through the continuous boundary conditions on which the interaction of the particles is considered. The accuracy of the theory and codes are verified by comparing results with those obtained for arbitrary plane wave incidence by CST simulation, and for ZOBB incidence by a numerical method. The effects of angle of incidence, pseudo-polarization angle, half-conical angle, beam center position, and permittivity tensor elements on the radar cross sections (RCSs) of several types of collective uniaxial anisotropic spheres, such as a linear chain, a 4×4×4 cube-shaped array, and other periodical structures consisting of massive spheres, are numerically analyzed. Selected results on the properties of typical particles such as TiO 2 , SiO 2 , or other particle lattices are calculated. This investigation could provide an effective test for further research on the scattering characteristics of an aggregate of anisotropic spheres by a high-order Bessel vortex beam. The results have important application in optical tweezers and particle manipulation. - Highlights: • Scattering of Bessel beam by an aggregate of uniaxial anisotropic spheres is studied. • The zero-order Bessel beam propagates and polarizes along arbitrary direction. • The accuracy of expansion coefficients, the scattering theory and codes is verified. • Effects of various parameters on scattering properties are numerically discussed. • Scattering properties of several type of periodical array are numerically analyzed.

Experimental generation of two-index Bessel-Gauss beams by engineering their angular spectrum functions

Science.gov (United States)

Yao, Hainan; Wang, Fei; Cai, Yangjian

2018-01-01

Two-index Bessel beams (TIBBs) was introduced by Ornigotti and Aiello (2014) theoretically. In this paper, we propose a simple experimental scheme for generation of two-index Bessel-Gauss beams (TIBGBs), as an extension of the TIBBs. The scheme is based on manipulating the amplitude and phase in the Fourier plane with the use of a spatial light modulator and a spiral phase plate. Furthermore, we experimentally report the generation of the several examples of the TIBGBs based on the proposed optical system. The focusing properties of the TIBGB with indices p = 1 and l = 2 passing through a single lens are investigated both theoretically and experimentally. The experimental results agree well with theoretical predictions.

Shape invariant higher-order Bessel-like beams carrying orbital angular momentum

CSIR Research Space (South Africa)

Ismail, Y

2012-09-01

Full Text Available -1 Journal of Optics September 2012/ Vol. 14 Shape invariant higher-order Bessel-like beams carrying orbital angular momentum Y Ismail1,2, N Khilo3, V Belyi3 and A Forbes1,2 1 School of Physics, University of KwaZulu-Natal, Private Bag X54001...

Axial acoustic radiation force on rigid oblate and prolate spheroids in Bessel vortex beams of progressive, standing and quasi-standing waves.

Science.gov (United States)

Mitri, F G

2017-02-01

The analysis using the partial-wave series expansion (PWSE) method in spherical coordinates is extended to evaluate the acoustic radiation force experienced by rigid oblate and prolate spheroids centered on the axis of wave propagation of high-order Bessel vortex beams composed of progressive, standing and quasi-standing waves, respectively. A coupled system of linear equations is derived after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. The system of linear equations depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated but converging PWSEs in the least-squares sense. Numerical results for the radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface, are computed with particular emphasis on the amplitude ratio describing the transition from the progressive to the pure standing waves cases, the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle and order of the Bessel vortex beam, as well as the dimensionless size parameter. A generalized expression for the radiation force function is derived for cases encompassing the progressive, standing and quasi-standing waves of Bessel vortex beams. This expression can be reduced to other types of beams/waves such as the zeroth-order Bessel non-vortex beam or the infinite plane wave case by appropriate selection of the beam parameters. The results for progressive waves reveal a tractor beam behavior, characterized by the emergence of an attractive pulling force acting in opposite direction of wave propagation. Moreover, the transition to the quasi-standing and pure standing wave cases shows the acoustical tweezers behavior in dual-beam Bessel vortex beams. Applications in acoustic levitation, particle manipulation and acousto

Quasi-ideal dynamics of vortex solitons embedded in flattop nonlinear Bessel beams.

Science.gov (United States)

Porras, Miguel A; Ramos, Francisco

2017-09-01

The applications of vortex solitons are severely limited by the diffraction and self-defocusing spreading of the background beam where they are nested. Nonlinear Bessel beams in self-defocusing media are nondiffracting, flattop beams where the nested vortex solitons can survive for propagation distances that are one order of magnitude larger than in the Gaussian or super-Gaussian beams. The dynamics of the vortex solitons is studied numerically and found to approach that in the ideal, uniform background, preventing vortex spiraling and decay, which eases vortex steering for applications.

Generation of J_0-Bessel-Gauss beam by a heterogeneous refractive index map

KAUST Repository

San Roman Alerigi, Damian

2012-07-01

In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to a J0-Bessel-Gauss convertor. We theoretically demonstrate the viability of a device that could be fabricated on a Si/Si1-yOy/Si1-x-yGexCy platform or by photo-refractive media. The proposed device is 200 ?m in length and 25 ?m in width, and its refractive index varies in controllable steps across the light propagation and transversal directions. The computed conversion efficiency and loss are 90%, and -0.457 dB, respectively. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction, demonstrate that a two-dimensional (2D) graded index map of the refractive index can be used to transform a Gauss beam into a J0-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping that is fully integrable in silicon photonics based planar lightwave circuits (PLCs). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and nonlinear beam diode lasers. © 2012 Optical Society of America.

Generation of J_0-Bessel-Gauss beam by a heterogeneous refractive index map

KAUST Repository

San Roman Alerigi, Damian; Alsunaidi, Mohammad; Ben Slimane, Ahmed; Ng, Tien Khee; Ooi, Boon S.; Zhang, Yaping

2012-01-01

In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to a J0-Bessel-Gauss convertor. We theoretically demonstrate the viability of a device that could be fabricated on a Si/Si1-yOy/Si1-x-yGexCy platform or by photo-refractive media. The proposed device is 200 ?m in length and 25 ?m in width, and its refractive index varies in controllable steps across the light propagation and transversal directions. The computed conversion efficiency and loss are 90%, and -0.457 dB, respectively. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction, demonstrate that a two-dimensional (2D) graded index map of the refractive index can be used to transform a Gauss beam into a J0-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping that is fully integrable in silicon photonics based planar lightwave circuits (PLCs). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and nonlinear beam diode lasers. © 2012 Optical Society of America.

Superpositions of higher-order bessel beams and nondiffracting speckle fields - (SAIP 2009)

CSIR Research Space (South Africa)

Dudley, Angela L

2009-07-01

Full Text Available speckle fields. The paper reports on illuminating a ring slit aperture with light which has an azimuthal phase dependence, such that the field produced is a superposition of two higher-order Bessel beams. In the case that the phase dependence of the light...

Interaction of a high-order Bessel beam with a submerged spherical ultrasound contrast agent shell - Scattering theory.

Science.gov (United States)

Mitri, F G

2010-03-01

Acoustic scattering properties of ultrasound contrast agents are useful in extending existing or developing new techniques for biomedical imaging applications. A useful first step in this direction is to investigate the acoustic scattering of a new class of acoustic beams, known as helicoidal high-order Bessel beams, to improve the understanding of their scattering characteristics by an ultrasound contrast agent, which at present is very limited. The transverse acoustic scattering of a commercially available albuminoidal ultrasound contrast agent shell filled with air or a denser gas such as perfluoropropane and placed in a helicoidal Bessel beam of any order is examined numerically. The shell is assumed to possess an outer radius a=3.5 microns and a thickness of approximately 105 nm. Moduli of the total and resonance transverse acoustic scattering form functions are numerically evaluated in the bandwidth 0scattering of a helicoidal Bessel beam of order m1 so that the dynamics of contrast agents would be significantly altered. The main finding of the present theory is the suppression or enhancement for a particular resonance that may be used to advantage in imaging with ultrasound contrast agents for clinical applications. 2009 Elsevier B.V. All rights reserved.

Wave-optics description of self-healing mechanism in Bessel beams.

Science.gov (United States)

Aiello, Andrea; Agarwal, Girish S

2014-12-15

Bessel beams' great importance in optics lies in that these propagate without spreading and can reconstruct themselves behind an obstruction placed across their path. However, a rigorous wave-optics explanation of the latter property is missing. In this work, we study the reconstruction mechanism by means of a wave-optics description. We obtain expressions for the minimum distance beyond the obstruction at which the beam reconstructs itself, which are in close agreement with the traditional one determined from geometrical optics. Our results show that the physics underlying the self-healing mechanism can be entirely explained in terms of the propagation of plane waves with radial wave vectors lying on a ring.

Generation of an elliptic hollow beam using Mathieu and Bessel functions.

Science.gov (United States)

Chakraborty, Rijuparna; Ghosh, Ajay

2006-09-01

A new (to our knowledge) technique for the generation of a propagation-invariant elliptic hollow beam is reported. It avoids the use of the radial Mathieu function and hence is mathematically simpler. Bessel functions with their arguments having elliptic locus are used to generate the mask, which is then recorded using holographic technique. To generate such an elliptic beam, both the angular Mathieu function, i.e., elliptic vortex term, and the expression for the circular vortex are used separately. The resultant mask is illuminated with a plane beam, and the proper filtering of its Fourier transform generates the expected elliptic beam. Results with both vortex terms are satisfactory. It has been observed that even for higher ellipticity the vortices do not separate.

Investigation of local spatial spectra of Bessel light beams

CSIR Research Space (South Africa)

Belyi, VN

2009-08-01

Full Text Available plane of lens and illuminated by plane wave. The superposition of plane waves in such scheme is proposed to be generated by point sources distributed within the circular diaphragm. In a case when diaphragm is placed outside of lens focus [2], Bessel... beam can be described as an image in lens of spherical waves superposition formed by some effective circular source in object plane of lens. In the scheme of BLB obtaining based on axicons, the appearance of superposition of plane waves can be studied...

Electromagnetic scattering of a vector Bessel beam in the presence of an impedance cone

KAUST Repository

Salem, Mohamed; Bagci, Hakan

2013-01-01

The electromagnetic field scattering of a vector Bessel beam in the presence of an infinite circular cone with an impedance boundary on its surface is considered. The impinging field is normal to the tip of the cone and is expanded in terms

Propagation-invariant vectorial Bessel beams by use of sub wavelength quantized Pancharatnam-Berry phase optics

International Nuclear Information System (INIS)

Niv, A.; Biener, G.; Kleiner, V.; Hasman, E.

2004-01-01

Full Text:Propagation-invariant scalar fields have been extensively studied both theoretically and experimentally, since they were proposed by Durnin et al. These fields were employed in applications such as optical tweezers and for transport and guiding of microspheres. Although there has recently been considerable theoretical interest in propagation-invariant vectorial beams, experimental studies of such beams have remained somewhat limited. One of the most interesting types of propagation-invariant vectorial beam is the linearly polarized axially symmetric beam (LPASB) [l]. Recently, we introduced and experimentally demonstrated propagation-invariant vectorial Bessel beams with linearly polarized axial symmetry based on quantized Pancharatnam-Berry phase optical elements (QPBOEs) [21 and an axicon. QP-BOEs utilize the geometric phase that accompanies space-variant polarization manipulations to achieve a desired phase modification [31. To test our approach we formed QPBOEs with different polarization orders as computer-generated space-variant sub wavelength gratings upon GaAs wafers for use with 10.6 micron laser radiation. The resultant beams were also transmitted through a polarizer that produced a unique propagation-invariant scalar beam. This beam has a propeller-shaped intensity pattern that can be rotated by simple rotation of the polarizer. We therefore have demonstrated the formation of a vectorial Bessel beam by using simple, lightweight thin elements and exploited that beam to perform a controlled rotation of a propeller-shaped intensity pattern that can be suitable for optical tweezers

Unified Bessel, Modified Bessel, Spherical Bessel and Bessel-Clifford Functions

OpenAIRE

Yaşar, Banu Yılmaz; Özarslan, Mehmet Ali

2016-01-01

In the present paper, unification of Bessel, modified Bessel, spherical Bessel and Bessel-Clifford functions via the generalized Pochhammer symbol [ Srivastava HM, Cetinkaya A, K{\\i}ymaz O. A certain generalized Pochhammer symbol and its applications to hypergeometric functions. Applied Mathematics and Computation, 2014, 226 : 484-491] is defined. Several potentially useful properties of the unified family such as generating function, integral representation, Laplace transform and Mellin tran...

Measuring a narrow Bessel beam spot by scanning a charge-coupled device (CCD) pixel

International Nuclear Information System (INIS)

Tiwari, S K; Ram, S P; Jayabalan, J; Mishra, S R

2010-01-01

By scanning a charge-coupled device (CCD) camera transverse to the beam axis and observing the variation in counts on a marked pixel, we demonstrate that we can measure a laser beam spot size smaller than the size of the CCD-pixel. We find this method particularly attractive for measuring the size of central spot of a Bessel beam, for which the established scanning knife-edge method does not work appropriately because of the large contribution of the rings surrounding the central spot to the signal

Transmission of a Bessel beam through a circular aperture in an impedance screen

International Nuclear Information System (INIS)

Umul, Yusuf Ziya

2014-01-01

The scattering effect of a circular aperture, located in an impedance plane, on a Bessel beam is investigated by decomposing the scattered wave into two subcomponents, namely the geometrical optics and diffracted fields. The diffracted waves are investigated with the aid of the geometrical theory of diffraction. The detour parameter is evaluated and the existence zones of the geometrical optics fields are determined. The various aspects of the reflected and transmitted scattered waves, including the self healing of the beam, are studied numerically. (letter)

Foreign Object Detection by Sub-Terahertz Quasi-Bessel Beam Imaging

Directory of Open Access Journals (Sweden)

Hyang Sook Chun

2012-12-01

Full Text Available Food quality monitoring, particularly foreign object detection, has recently become a critical issue for the food industry. In contrast to X-ray imaging, terahertz imaging can provide a safe and ionizing-radiation-free nondestructive inspection method for foreign object sensing. In this work, a quasi-Bessel beam (QBB known to be nondiffracting was generated by a conical dielectric lens to detect foreign objects in food samples. Using numerical evaluation via the finite-difference time-domain (FDTD method, the beam profiles of a QBB were evaluated and compared with the results obtained via analytical calculation and experimental characterization (knife edge method, point scanning method. The FDTD method enables a more precise estimation of the beam profile. Foreign objects in food samples, namely crickets, were then detected with the QBB, which had a deep focus and a high spatial resolution at 210 GHz. Transmitted images using a Gaussian beam obtained with a conventional lens were compared in the sub-terahertz frequency experimentally with those using a QBB generated using an axicon.

Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces

International Nuclear Information System (INIS)

David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth

2015-01-01

We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape

Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces

Energy Technology Data Exchange (ETDEWEB)

David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth, E-mail: rsignorell@ethz.ch [Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich (Switzerland)

2015-04-21

We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.

Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces.

Science.gov (United States)

David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth

2015-04-21

We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.

Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces

Science.gov (United States)

David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth

2015-04-01

We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.

Experiments with BECs in a Painted Potential: Atom SQUID, Matter Wave Bessel Beams, and Matter Wave Circuits

Science.gov (United States)

Boshier, Malcolm; Ryu, Changhyun; Blackburn, Paul; Blinova, Alina; Henderson, Kevin

2014-05-01

The painted potential is a time-averaged optical dipole potential which is able to create arbitrary and dynamic two dimensional potentials for Bose Einstein condensates (BECs). This poster reports three recent experiments using this technique. First, we have realized the dc atom SQUID geometry of a BEC in a toroidal trap with two Josephson junctions. We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. Second, we have used free expansion of a rotating toroidal BEC to create matter wave Bessel beams, which are of interest because perfect Bessel beams (plane waves with amplitude profiles described by Bessel functions) propagate without diffraction. Third, we have realized the basic circuit elements necessary to create complex matter wave circuits. We launch BECs at arbitrary velocity along straight waveguides, propagate them around curved waveguides and stadium-shaped waveguide traps, and split them coherently at y-junctions that can also act as switches. Supported by LANL/LDRD.

Acoustical radiation torque and force for spheres and Bessel beam extinction efficiency

Science.gov (United States)

Marston, Philip L.; Zhang, Likun

2014-11-01

The scattering of optical and acoustical beams is relevant to the levitation and manipulation of drops. Here we examine theoretical developments in the acoustical case. We previously showed how the optical theorem for extinction can be extended to invariant beams. The example of a sphere in a Bessel beam facilitates the direct comparison with a circular disc computed using Babinet's principle and the Kirchhoff approximation. In related work, by considering traveling or standing wave first-order vortex beams we previously showed that the radiation torque is the ratio of the absorbed power and the radian acoustic frequency. By modifying the scattering to account for the viscosity of the surrounding fluid in the analysis of the absorbed power, approximations for radiation torque and force are obtained at long wavelengths in special cases and these can be compared with results published elsewhere.

Measurement of Rayleigh Wave Beams Using Angle Beam Wedge Transducers as the Transmitter and Receiver with Consideration of Beam Spreading.

Science.gov (United States)

Zhang, Shuzeng; Li, Xiongbing; Jeong, Hyunjo

2017-06-20

A theoretical model, along with experimental verification, is developed to describe the generation, propagation and reception of a Rayleigh wave using angle beam wedge transducers. The Rayleigh wave generation process using an angle beam wedge transducer is analyzed, and the actual Rayleigh wave sound source distributions are evaluated numerically. Based on the reciprocity theorem and considering the actual sound source, the Rayleigh wave beams are modeled using an area integral method. The leaky Rayleigh wave theory is introduced to investigate the reception of the Rayleigh wave using the angle beam wedge transducers, and the effects of the wave spreading in the wedge and transducer size are considered in the reception process. The effects of attenuations of the Rayleigh wave and leaky Rayleigh wave are discussed, and the received wave results with different sizes of receivers are compared. The experiments are conducted using two angle beam wedge transducers to measure the Rayleigh wave, and the measurement results are compared with the predictions using different theoretical models. It is shown that the proposed model which considers the wave spreading in both the sample and wedges can be used to interpret the measurements reasonably.

Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid

OpenAIRE

Mitri, F. G.

2015-01-01

Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (\\theta = \\pi) in the near-field an...

Debye series analysis of internal and near-surface fields for a homogeneous sphere illuminated by an axicon-generated vector Bessel beam

International Nuclear Information System (INIS)

Qin, Shitong; Li, Renxian; Yang, Ruiping; Ding, Chunying

2017-01-01

The interaction of an axicon-generated vector Bessel beam (AGVBB) with a homogeneous sphere is investigated in the framework of generalized Lorenz-Mie theory (GLMT). An analytical expression of beam shape coefficients (BSCs) is derived using angular spectrum decomposition method (ASDM), and the scattering coefficients are expanded using Debye series (DSE) in order to isolate the contribution of single scattering process. The internal and near-surface electric fields are numerically analyzed, and the effect of beam location, polarization, order of beam, half-cone angle, and scattering process (namely Debye mode p) are mainly discussed. Numerical results show that a curve formed by extreme peaks can be observed, and the electric fields can be locally enhanced after the interaction of AGVBBs with the particle. Internal and near-surface fields, especially its local enhancement, are very sensitive to the beam parameters, including polarization, order, half-cone angle, etc. The internal fields can also be enhanced by various scattering process (or Debye mode p). Such results have important applications in various fields, including particle sizing, optical tweezers, etc. - Highlights: • Debye series is employed to the analysis of internal and near-surface fields for a sphere illuminated by a vector Bessel beam. • Analytical expressions of BSCs for vector Bessel beams with selected polarizations are derived using ASDM. • The local enhancement of internal and near-surface fields is investigated. • The polarization, order, half-cone angle of the beam affect the local enhancement. • The local enhancement of internal fields is sensitive to the scattering process.

Measurement of the orbital angular momentum density of Bessel beams by projection into a Laguerre–Gaussian basis

CSIR Research Space (South Africa)

Schulze, C

2014-09-01

Full Text Available We present the measurement of the orbital angular momentum (OAM) density of Bessel beams and superpositions thereof by projection into a Laguerre–Gaussian basis. This projection is performed by an all-optical inner product measurement performed...

Propagation of Bessel-Gaussian beams through a double-apertured fractional Fourier transform optical system.

Science.gov (United States)

Tang, Bin; Jiang, Chun; Zhu, Haibin

2012-08-01

Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.

Nonparaxial Bessel and Bessel–Gauss pincers light-sheets

Energy Technology Data Exchange (ETDEWEB)

Mitri, F.G., E-mail: F.G.Mitri@ieee.org

2017-01-23

Highlights: • Bessel and Bessel–Gauss autofocusing light sheets (i.e. beams in 2D) are developed. • The light-sheets are synthesized based on the angular spectrum decomposition method. • Computations of the scattering, radiation force and torque benefit from the solutions. - Abstract: Nonparaxial optical Bessel and Bessel–Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.

Nonparaxial Bessel and Bessel–Gauss pincers light-sheets

International Nuclear Information System (INIS)

Mitri, F.G.

2017-01-01

Highlights: • Bessel and Bessel–Gauss autofocusing light sheets (i.e. beams in 2D) are developed. • The light-sheets are synthesized based on the angular spectrum decomposition method. • Computations of the scattering, radiation force and torque benefit from the solutions. - Abstract: Nonparaxial optical Bessel and Bessel–Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.

Stored polarized beams: MILES, LIMES, SMILE, sine-Bessels and SODOM2 too

International Nuclear Information System (INIS)

Mane, S.R.

2008-01-01

The fundamental theory underlying several computational algorithms for the spin dynamics of stored polarized beams is analyzed. Particular attention is paid to the consequences of the use of finite-dimensional matrices and/or Fourier series. The single resonance model with a pair of diametrically opposed nonorthogonal pointlike Siberian Snakes is analyzed in detail to clarify several points pertaining to the above algorithms, and more generally to the spin dynamics of stored polarized beams in rings with Snakes. New analytical results are also presented, e.g. for the spin tune shift in the nonorthogonal Snakes model, and the sine-Bessel functions for the orthogonal Snakes model. Many results are derived using multiple algorithms, which serves as a check on their mutual consistency

Acoustics of finite asymmetric exotic beams: Examples of Airy and fractional Bessel beams

Science.gov (United States)

Mitri, F. G.

2017-12-01

The purpose of this investigation is to examine the properties of finite asymmetric exotic scalar (acoustic) beams with unusual properties using the angular spectrum decomposition in plane waves. Such beams possess intrinsic uncommon characteristics that make them attractive from the standpoint of particle manipulation, handling and rotation, and possibly other applications in particle clearing and separation. Assuming a specific apodization function at the acoustic source, the angular spectrum function is calculated and used to synthesize the radiated pressure field (i.e., excluding evanescent waves that decay away from the source) in the forward direction of wave motion (i.e., away from the source). Moreover, a generalized hybrid method combining the angular spectrum approach with the multipole expansion formalism in spherical coordinates is developed, which is applicable to any finite beam of arbitrary wavefront. The improved approach allows adequate computation of the resonance scattering, radiation force, and spin torque components on an object of arbitrary shape, located on or off the axis of the incident beam in space. Considering the illustrative example of a viscous fluid sphere submerged in a non-viscous liquid and illuminated by finite asymmetric beams such as the Airy and the Bessel vortex beam with fractional order, numerical computations for the scattering, radiation force, and torque components are performed with an emphasis on the distance from the source, the arbitrary location of the particle ,and the asymmetric nature of the incident field. Moreover, beamforming calculations are presented with supplementary animations for the pressure field distribution in space, with an emphasis on the intrinsic properties of the selected beams. The numerical predictions illustrate the scattering, radiation force, and spin torque properties depending on the beam parameters and the distance separating the sphere from the source. This study provides a generalized

Improved fixation quality provided by a Bessel beacon in an adaptive optics system.

Science.gov (United States)

Lambert, Andrew J; Daly, Elizabeth M; Dainty, Christopher J

2013-07-01

We investigate whether a structured probe beam that creates the beacon for use in a retinal imaging adaptive optics system can provide useful side effects. In particular we investigate whether a Bessel beam that is seen by the subject as a set of concentric rings has a dampening effect on fixation variations of the subject under observation. This calming effect would allow longer periods of observation, particularly for patients with abnormal fixation. An experimental adaptive optics system developed for retinal imaging is used to monitor the fluctuations in aberrations for artificial and human subjects. The probe beam is alternated between a traditional beacon and one provided by a Bessel beam created by SLM. Time-frequency analysis is used to indicate the differences in power and time variation during fixation depending on whether the Bessel beam or the traditional beacon is employed. Comparison is made with the response for an artificial eye to discount systemic variations. Significant evidence is accrued to indicate the reduced fluctuations in fixation when the Bessel beam is employed to create the beacon. © 2013 The Authors Ophthalmic & Physiological Optics © 2013 The College of Optometrists.

Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media.

Science.gov (United States)

Fahrbach, Florian O; Rohrbach, Alexander

2012-01-17

Laser beams that can self-reconstruct their initial beam profile even in the presence of massive phase perturbations are able to propagate deeper into inhomogeneous media. This ability has crucial advantages for light sheet-based microscopy in thick media, such as cell clusters, embryos, skin or brain tissue or plants, as well as scattering synthetic materials. A ring system around the central intensity maximum of a Bessel beam enables its self-reconstruction, but at the same time illuminates out-of-focus regions and deteriorates image contrast. Here we present a detection method that minimizes the negative effect of the ring system. The beam's propagation stability along one straight line enables the use of a confocal line principle, resulting in a significant increase in image contrast. The axial resolution could be improved by nearly 100% relative to the standard light-sheet techniques using scanned Gaussian beams, while demonstrating self-reconstruction also for high propagation depths.

Fourier optics along a hybrid optical fiber for Bessel-like beam generation and its applications in multiple-particle trapping.

Science.gov (United States)

Kim, Jongki; Jeong, Yoonseob; Lee, Sejin; Ha, Woosung; Shin, Jeon-Soo; Oh, Kyunghwan

2012-02-15

Highly efficient Bessel-like beam generation was achieved based on a new all-fiber method that implements Fourier transformation of a micro annular aperture along a concatenated composite optical fiber. The beam showed unique characteristics of tilted washboard optical potential in the transverse plane and sustained a nondiffracting length over 400 μm along the axial direction. Optical trapping of multiple dielectric particles and living Jurkat cells were successfully demonstrated along the axial direction of the beam in the water.

Conformable Fractional Bessel Equation and Bessel Functions

OpenAIRE

Gökdoğan, Ahmet; Ünal, Emrah; Çelik, Ercan

2015-01-01

In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary solutions. In addition, we present certain property of fractional Bessel functions.

The Generation Mechanism of Airy—Bessel Wave Packets in Free Space

International Nuclear Information System (INIS)

Ren Zhi-Jun; Ying Chao-Fu; Fan Chang-Jiang; Wu Qiong

2012-01-01

Localized optical Airy—Bessel configuration wave packets were first generated on the basis of a grating-telescope combination [Nat. Photon. 4(2010) 103]. By studying the spatially induced group velocity dispersion effect of ultrashort pulsed Bessel beams during propagation, we find the universal physical foundation of generating Airy—Bessel wave packets (ABWs) in free space. The research results are expected to open up more common channels for generating stable linear localized ABWs

Annular spherically focused ring transducers for improved single-beam acoustical tweezers

Energy Technology Data Exchange (ETDEWEB)

Mitri, F. G., E-mail: F.G.Mitri@ieee.org [Chevron, Area 52 Technology—ETC, Santa Fe, New Mexico 87508 (United States)

2016-02-14

The use of ultrasonic transducers with a central hollow is suggested for improved single-beam acoustical tweezers applications. Within the framework of the Fresnel-Kirchhoff parabolic approximation, a closed-form partial-wave series expansion (PWSE) for the incident velocity potential (or pressure) field is derived for an annular spherically focused ring (asfr) with uniform vibration across its surface in spherical coordinates. The Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions are used to obtain the PWSE assuming a weakly focused beam (with a focusing angle α ≤ 20°). The PWSE allows evaluating the incident field from the finite asfr in 3D. Moreover, the obtained solution allows computing efficiently the acoustic scattering and radiation force on a sphere centered on the beam's axis of wave propagation. The analytical solution is valid for wavelengths largely exceeding the radius of the asfr and when the viscosity of the surrounding fluid can be neglected. Numerical predictions for the beam-forming, scattering, and axial time-averaged radiation force are performed with particular emphasis on the asfr thickness, the axial distance separating the sphere from the center of the transducer, the (non-dimensional) size of the transducer, as well as the sphere's elastic properties without restriction to the long- (i.e., Rayleigh) or the short-wavelength (i.e., ray acoustics) regimes. Potential applications of the present solution are in beam-forming design, particle tweezing, and manipulation due to negative forces using ultrasonic asfr transducers.

Testing of electron beam welding by ultrasonic transducers

International Nuclear Information System (INIS)

Touffait, A.-M.; Roule, M.; Destribats, M.-T.

1978-01-01

Focalized ultrasonic testing is well adapted to the study of electron beam welding. This type of welding leads to narrow weld beads and to small dimension testing zones. Focalized transducers can be used enabling very small defects to be detected [fr

Analysis of ultrasonic beam profile due to change of elements' number for phased array transducer (part 2)

International Nuclear Information System (INIS)

Choi, Sang Woo; Lee, Joon Hyun

1998-01-01

The phased array offers many advantages and improvements over conventional single-element transducers such as the straight-beam and angle-beam. The advantages of array sensors for large structures are two folds; firstly, array transducers provide a method of rapid beam steering and sequential addressing of a large area of interest without requiring mechanical or manual scanning which is particularly important in real-time application. Secondly, array transducer provide a method of dynamic focusing, in which the focal length of the ultrasonic beam varies as the pulse propagates through the material. There are some parameters such as number, size, center to center space of elements to design phased array transducer. In previous study. the characteristics of beam steering and dynamic focusing had been simulated for ultrasonic SH-wave with varying the number of phased array transducer's element. In this study, the characteristic of beam steering for phased array transducer has been simulated for ultrasonic SH-wave on the basis of Huygen's principle with varying center to center space of elements. Ultrasonic beam directivity and focusing due to change of time delay of each element were discussed with varying center to center space of elements.

Theory of Bessel Functions of High Rank - I: Fundamental Bessel Functions

OpenAIRE

Qi, Zhi

2014-01-01

In this article we introduce a new category of special functions called fundamental Bessel functions arising from the Voronoi summation formula for $\\mathrm{GL}_n (\\mathbb{R})$. The fundamental Bessel functions of rank one and two are the oscillatory exponential functions $e^{\\pm i x}$ and the classical Bessel functions respectively. The main implements and subjects of our study of fundamental Bessel functions are their formal integral representations and Bessel equations.

Two-photon optics of Bessel-Gaussian modes

CSIR Research Space (South Africa)

McLaren, M

2013-09-01

Full Text Available In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum...

Bessel light sheet structured illumination microscopy

Science.gov (United States)

Noshirvani Allahabadi, Golchehr

Biomedical study researchers using animals to model disease and treatment need fast, deep, noninvasive, and inexpensive multi-channel imaging methods. Traditional fluorescence microscopy meets those criteria to an extent. Specifically, two-photon and confocal microscopy, the two most commonly used methods, are limited in penetration depth, cost, resolution, and field of view. In addition, two-photon microscopy has limited ability in multi-channel imaging. Light sheet microscopy, a fast developing 3D fluorescence imaging method, offers attractive advantages over traditional two-photon and confocal microscopy. Light sheet microscopy is much more applicable for in vivo 3D time-lapsed imaging, owing to its selective illumination of tissue layer, superior speed, low light exposure, high penetration depth, and low levels of photobleaching. However, standard light sheet microscopy using Gaussian beam excitation has two main disadvantages: 1) the field of view (FOV) of light sheet microscopy is limited by the depth of focus of the Gaussian beam. 2) Light-sheet images can be degraded by scattering, which limits the penetration of the excitation beam and blurs emission images in deep tissue layers. While two-sided sheet illumination, which doubles the field of view by illuminating the sample from opposite sides, offers a potential solution, the technique adds complexity and cost to the imaging system. We investigate a new technique to address these limitations: Bessel light sheet microscopy in combination with incoherent nonlinear Structured Illumination Microscopy (SIM). Results demonstrate that, at visible wavelengths, Bessel excitation penetrates up to 250 microns deep in the scattering media with single-side illumination. Bessel light sheet microscope achieves confocal level resolution at a lateral resolution of 0.3 micron and an axial resolution of 1 micron. Incoherent nonlinear SIM further reduces the diffused background in Bessel light sheet images, resulting in

Electromagnetic scattering of a vector Bessel beam in the presence of an impedance cone

KAUST Repository

Salem, Mohamed

2013-07-01

The electromagnetic field scattering of a vector Bessel beam in the presence of an infinite circular cone with an impedance boundary on its surface is considered. The impinging field is normal to the tip of the cone and is expanded in terms of vector spherical wave functions; a Kontorovich-Lebedev (KL) transform is employed to expand the scattered fields. The problem is reduced to a singular integral equation with a variable coefficient of the non-convolution type. The singularities of the spectral function are deduced and representations for the field at the tip of the cone as well as other regions are given together with the conditions of validity of these representations. © 2013 IEEE.

Unfocused beam patterns in nonattenuating and attenuating fluids

International Nuclear Information System (INIS)

Goldstein, Albert

2004-01-01

The most important aspect of an ultrasound measuring system is knowledge of the transducer beam pattern. At all depths accurate single integral equations have been derived for the full beam pattern of steady state unfocused circular flat piston sources radiating into nonattenuating and attenuating fluids. The axial depth of the beginning of the unattenuated beam pattern far field is found to be at 6.41Y 0 . The unattenuated single integral equations are identical to a Jinc function directivity term at this and deeper depths. For attenuating fluids values of α and z are found that permit the attenuated axial pressure to be represented by a plane wave multiplicative exponential attenuation factor. This knowledge will aid in the experimental design of highly accurate attenuation measurements. Accurate single integral equations for the attenuated full beam pattern are derived using complex Bessel functions

Gradient forces on double-negative particles in optical tweezers using Bessel beams in the ray optics regime.

Science.gov (United States)

Ambrosio, Leonardo A; Hernández-Figueroa, Hugo E

2010-11-08

Gradient forces on double negative (DNG) spherical dielectric particles are theoretically evaluated for v-th Bessel beams supposing geometrical optics approximations based on momentum transfer. For the first time in the literature, comparisons between these forces for double positive (DPS) and DNG particles are reported. We conclude that, contrary to the conventional case of positive refractive index, the gradient forces acting on a DNG particle may not reverse sign when the relative refractive index n goes from |n|>1 to |n|<1, thus revealing new and interesting trapping properties.

Computational study of scattering of a zero-order Bessel beam by large nonspherical homogeneous particles with the multilevel fast multipole algorithm

Science.gov (United States)

Yang, Minglin; Wu, Yueqian; Sheng, Xinqing; Ren, Kuan Fang

2017-12-01

Computation of scattering of shaped beams by large nonspherical particles is a challenge in both optics and electromagnetics domains since it concerns many research fields. In this paper, we report our new progress in the numerical computation of the scattering diagrams. Our algorithm permits to calculate the scattering of a particle of size as large as 110 wavelengths or 700 in size parameter. The particle can be transparent or absorbing of arbitrary shape, smooth or with a sharp surface, such as the Chebyshev particles or ice crystals. To illustrate the capacity of the algorithm, a zero order Bessel beam is taken as the incident beam, and the scattering of ellipsoidal particles and Chebyshev particles are taken as examples. Some special phenomena have been revealed and examined. The scattering problem is formulated with the combined tangential formulation and solved iteratively with the aid of the multilevel fast multipole algorithm, which is well parallelized with the message passing interface on the distributed memory computer platform using the hybrid partitioning strategy. The numerical predictions are compared with the results of the rigorous method for a spherical particle to validate the accuracy of the approach. The scattering diagrams of large ellipsoidal particles with various parameters are examined. The effect of aspect ratios, as well as half-cone angle of the incident zero-order Bessel beam and the off-axis distance on scattered intensity, is studied. Scattering by asymmetry Chebyshev particle with size parameter larger than 700 is also given to show the capability of the method for computing scattering by arbitrary shaped particles.

Simulation of 3-D radiation beam patterns propagated through a planar interface from ultrasonic phased array transducers.

Science.gov (United States)

Song, Sung-Jin; Kim, Chang-Hwan

2002-05-01

Phased array transducers are quite often mounted on solid wedges with specific angles in many practical ultrasonic inspections of thin plates phased array techniques with testing set-up, it is essential to have thorough understanding on the characteristics of radiation beam pattern produced in the interrogated medium. To address such a need, this paper proposes a systematic way to calculate full 3-D radiation beam patterns produced in the interrogated solid medium by phased array transducers mounted on a solid wedge. In order to investigate the characteristics of radiation beam patterns in steel, simulation is carried out for 7.5 MHz array transducers mounted on an acrylic wedge with the angle of 15.45 degrees with various of steering angles and/or focal planes.

Spherical Bessel transform via exponential sum approximation of spherical Bessel function

Science.gov (United States)

Ikeno, Hidekazu

2018-02-01

A new algorithm for numerical evaluation of spherical Bessel transform is proposed in this paper. In this method, the spherical Bessel function is approximately represented as an exponential sum with complex parameters. This is obtained by expressing an integral representation of spherical Bessel function in complex plane, and discretizing contour integrals along steepest descent paths and a contour path parallel to real axis using numerical quadrature rule with the double-exponential transformation. The number of terms in the expression is reduced using the modified balanced truncation method. The residual part of integrand is also expanded by exponential functions using Prony-like method. The spherical Bessel transform can be evaluated analytically on arbitrary points in half-open interval.

On numerical Bessel transformation

International Nuclear Information System (INIS)

Sommer, B.; Zabolitzky, J.G.

1979-01-01

The authors present a computer program to calculate the three dimensional Fourier or Bessel transforms and definite integrals with Bessel functions. Numerical integration of systems containing Bessel functions occurs in many physical problems, e.g. electromagnetic form factor of nuclei, all transitions involving multipole expansions at high momenta. Filon's integration rule is extended to spherical Bessel functions. The numerical error is of the order of the Simpson error term of the function which has to be transformed. Thus one gets a stable integral even at large arguments of the transformed function. (Auth.)

Symmetric q-Bessel functions

Directory of Open Access Journals (Sweden)

Giuseppe Dattoli

1996-05-01

Full Text Available q analog of bessel functions, symmetric under the interchange of q and q^ −1 are introduced. The definition is based on the generating function realized as product of symmetric q-exponential functions with appropriate arguments. Symmetric q-Bessel function are shown to satisfy various identities as well as second-order q-differential equations, which in the limit q → 1 reproduce those obeyed by the usual cylindrical Bessel functions. A brief discussion on the possible algebraic setting for symmetric q-Bessel functions is also provided.

Two-dimensional analytic modeling of acoustic diffraction for ultrasonic beam steering by phased array transducers.

Science.gov (United States)

Wang, Tiansi; Zhang, Chong; Aleksov, Aleksandar; Salama, Islam; Kar, Aravinda

2017-04-01

Phased array ultrasonic transducers enable modulating the focal position of the acoustic waves, and this capability is utilized in many applications, such as medical imaging and non-destructive testing. This type of transducers also provides a mechanism to generate tilted wavefronts in acousto-optic deflectors to deflect laser beams for high precision advanced laser material processing. In this paper, a theoretical model is presented for the diffraction of ultrasonic waves emitted by several phased array transducers into an acousto-optic medium such as TeO 2 crystal. A simple analytic expression is obtained for the distribution of the ultrasonic displacement field in the crystal. The model prediction is found to be in good agreement with the results of a numerical model that is based on a non-paraxial multi-Gaussian beam (NMGB) model. Published by Elsevier B.V.

Semi-analytical computation of the acoustic field of a segment of a cylindrically concave transducer in lossless and attenuating media.

Science.gov (United States)

Karbeyaz, Başak Ulker; Miller, Eric L; Cleveland, Robin O

2007-02-01

Conventional ultrasound transducers used for medical diagnosis generally consist of linearly aligned rectangular apertures with elements that are focused in one plane. While traditional beamforming is easily accomplished with such transducers, the development of quantitative, physics-based imaging methods, such as tomography, requires an accurate, and computationally efficient, model of the field radiated by the transducer. The field can be expressed in terms of the Helmholtz-Kirchhoff integral; however, its direct numerical evaluation is a computationally intensive task. Here, a fast semianalytical method based on Stepanishen's spatial impulse response formulation [J. Acoust. Soc. Am. 49, 1627-1638 (1971)] is developed to compute the acoustic field of a rectangular element of cylindrically concave transducers in a homogeneous medium. The pressure field, for, lossless and attenuating media, is expressed as a superposition of Bessel functions, which can be evaluated rapidly. In particular, the coefficients of the Bessel series are frequency independent and need only be evaluated once for a given transducer. A speed up of two orders of magnitude is obtained compared to an optimized direct numerical integration. The numerical results are compared with Field II and the Fresnel approximation.

Inequalities for the Modified k-Bessel Function

Directory of Open Access Journals (Sweden)

Saiful Rahman Mondal

2017-07-01

Full Text Available The article considers the generalized k-Bessel functions and represents it as Wright functions. Then we study the monotonicity properties of the ratio of two different orders k- Bessel functions, and the ratio of the k-Bessel and the k-Bessel functions. The log-convexity with respect to the order of the k-Bessel also given. An investigation regarding the monotonicity of the ratio of the k-Bessel and k-confluent hypergeometric functions are discussed.

Bessel functions

CERN Document Server

Nambudiripad, K B M

2014-01-01

After presenting the theory in engineers' language without the unfriendly abstraction of pure mathematics, several illustrative examples are discussed in great detail to see how the various functions of the Bessel family enter into the solution of technically important problems. Axisymmetric vibrations of a circular membrane, oscillations of a uniform chain, heat transfer in circular fins, buckling of columns of varying cross-section, vibrations of a circular plate and current density in a conductor of circular cross-section are considered. The problems are formulated purely from physical considerations (using, for example, Newton's law of motion, Fourier's law of heat conduction electromagnetic field equations, etc.) Infinite series expansions, recurrence relations, manipulation of expressions involving Bessel functions, orthogonality and expansion in Fourier-Bessel series are also covered in some detail. Some important topics such as asymptotic expansions, generating function and Sturm-Lioville theory are r...

Resonant and hollow beam generation of plasma channels

International Nuclear Information System (INIS)

Alexeev, I.; Kim, K.Y.; Fan, J.; Parra, E.; Milchberg, H.M.; Margolin, L.Ya.; Pyatnitskii, L.N.

2001-01-01

We report two variations on plasma channel generation using the propagation of intense Bessel beams. In the first experiment, the propagation of a high intensity Bessel beam in neutral gas is observed to give rise to resonantly enhanced plasma channel generation, resulting from resonant self-trapping of the beam and enhanced laser-plasma heating. In the second experiment, a high power, hollow Bessel beam (J 5 ) is produced and the optical breakdown of a gas target and the generation of a tubular plasma channel with such a beam is realized for the first time. Hydrodynamic simulations of the laser-plasma interaction of are in good agreement with the results of both experiments

Integrals of Bessel functions

OpenAIRE

Babusci, D.; Dattoli, G.; Germano, B.; Martinelli, M. R.; Ricci, P. E.

2011-01-01

We use the operator method to evaluate a class of integrals involving Bessel or Bessel-type functions. The technique we propose is based on the formal reduction of these family of functions to Gaussians.

Bessel Weighted Asymmetries

Energy Technology Data Exchange (ETDEWEB)

Avakian, Harut [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Gamberg, Leonard [Pennsylvania State Univ., University Park, PA (United States); Rossi, Patrizia [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Prokudin, Alexei [Pennsylvania State Univ., University Park, PA (United States)

2016-05-01

We review the concept of Bessel weighted asymmetries for semi-inclusive deep inelastic scattering and focus on the cross section in Fourier space, conjugate to the outgoing hadron’s transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. The procedure is applied to studies of the double longitudinal spin asymmetry in semi-inclusive deep inelastic scattering using a new dedicated Monte Carlo generator which includes quark intrinsic transverse momentum within the generalized parton model. We observe a few percent systematic offset of the Bessel-weighted asymmetry obtained from Monte Carlo extraction compared to input model calculations, which is due to the limitations imposed by the energy and momentum conservation at the given energy and hard scale Q2. We find that the Bessel weighting technique provides a powerful and reliable tool to study the Fourier transform of TMDs with controlled systematics due to experimental acceptances and resolutions with different TMD model inputs.

Investigation of focused and unfocused transducer beam patterns in moderately nonlinear absorbing media

Science.gov (United States)

Kharin, Nikolay A.

2001-05-01

The novel solution of the KZK equation for acoustic pressure of the second harmonic in slightly focused beam of a circular transducer was obtained in a closed form for moderately nonlinear absorbing media (Gol'dberg numbers ~ 1). The solution is based on the method of slowly changing wave profile in combination with the method of successive approximations. Two pairs of transducers (Valpey-Fisher Corp.) Were compared to investigate the influence of focusing on the applicability of the moderate nonlinearity approach. The first pair was of 0.25' diameter and the second was of 0.5' diameter. Both pairs has one transducer with flat surface and the other geometrically focused at 4'. The central frequency for all transducers was 5 MHz. Measurements were undertaken in the blood-mimicking solution of water and glycerine. The results demonstrated that for slightly focused transducers with circular apertures, the moderate nonlinearity approach is still valid, as it was proved for flat sources with the same source level, despite the higher pressures in the focal region. The peak pressure for the weakly focused system occurs at a shorter range than focal length.

Instantaneous axial force of a high-order Bessel vortex beam of acoustic waves incident upon a rigid movable sphere.

Science.gov (United States)

Mitri, F G; Fellah, Z E A

2011-08-01

The present investigation examines the instantaneous force resulting from the interaction of an acoustical high-order Bessel vortex beam (HOBVB) with a rigid sphere. The rigid sphere case is important in fluid dynamics applications because it perfectly simulates the interaction of instantaneous sound waves in a reduced gravity environment with a levitated spherical liquid soft drop in air. Here, a closed-form solution for the instantaneous force involving the total pressure field as well as the Bessel beam parameters is obtained for the case of progressive, stationary and quasi-stationary waves. Instantaneous force examples for progressive waves are computed for both a fixed and a movable rigid sphere. The results show how the instantaneous force per unit cross-sectional surface and unit pressure varies versus the dimensionless frequency ka (k is the wave number in the fluid medium and a is the sphere's radius), the half-cone angle β and the order m of the HOBVB. It is demonstrated here that the instantaneous force is determined only for (m,n) = (0,1) (where n is the partial-wave number), and vanishes for m>0 because of symmetry. In addition, the instantaneous force and normalized amplitude velocity results are computed and compared with those of a rigid immovable (fixed) sphere. It is shown that they differ significantly for ka values below 5. The proposed analysis may be of interest in the analysis of instantaneous forces on spherical particles for particle manipulation, filtering, trapping and drug delivery. The presented solutions may also serve as a method for comparison to other solutions obtained by strictly numerical or asymptotic approaches. Copyright © 2011 Elsevier B.V. All rights reserved.

Walk-off reduction, using an external optical plate and Bessel-Gaussian interaction

Science.gov (United States)

Masoume, Mansouri; Mohsen, Askarbioki; Saeed Ghavami, Sabouri; Alireza, Khorsandi

2015-02-01

To reduce the walk-off angle of the extraordinary third-harmonic ultraviolet wave at 355 nm generated by type II KTiOPO4 and type I β-BaB2O4 optical crystals, and the Gaussian output beam of a Q-switched Nd:YAG laser, a simple theoretical model was developed based on a rotatable BK7 plate of variable thickness. By rotating the plate up to 35° along the beam direction, we reduced the walk-off angle up to ˜ 13%. The same phenomenon is predicted by the model, confirming the performance of the model. It is found that, due to the walk-off effect, the intensity profile of the third-harmonic generation beam is slightly degraded. To compensate for the observed phenomena and further reduce the walk-off, we used a combination of a convex lens and an axicon to transform the beam profile of the interacting fundamental and second-harmonic generation waves to the zero-order Bessel-Gaussian form. As a result, the walk-off is decreased to ˜48.81 mrad, providing ˜30% relative reduction. By using the same BK7 plate rotated up to 35° along the third-harmonic beam direction, the walk-off angle is further reduced to 38.9 mrad. Moreover, it is observed that the beam profile of the emerged Bessel-Gaussian third-harmonic generation beam remains unchanged with no degradation.

Ultrahigh-sensitive multimode interference-based fiber optic liquid-level sensor realized using illuminating zero-order Bessel-Gauss beam

Science.gov (United States)

Saha, Ardhendu; Datta, Arijit; Kaman, Surjit

2018-03-01

A proposal toward the enhancement in the sensitivity of a multimode interference-based fiber optic liquid-level sensor is explored analytically using a zero-order Bessel-Gauss (BG) beam as the input source. The sensor head consists of a suitable length of no-core fiber (NCF) sandwiched between two specialty high-order mode fibers. The coupling efficiency of various order modes inside the sensor structure is assessed using guided-mode propagation analysis and the performance of the proposed sensor has been benchmarked against the conventional sensor using a Gaussian beam. Furthermore, the study has been corroborated using a finite-difference beam propagation method in Lumerical's Mode Solutions software to investigate the propagation of the zero-order BG beam inside the sensor structure. Based on the simulation outcomes, the proposed scheme yields a maximum absolute sensitivity of up to 3.551 dB / mm and a sensing resolution of 2.816 × 10 - 3 mm through the choice of an appropriate length of NCF at an operating wavelength of 1.55 μm. Owing to this superior sensing performance, the reported sensing technology expedites an avenue to devise a high-performance fiber optic-level sensor that finds profound implication in different physical, biological, and chemical sensing purposes.

Numerical Analysis of Ultrasonic Beam Profile Due to the Change of the Number of Piezoelectric Elements for Phased Array Transducer

International Nuclear Information System (INIS)

Choi, Sang Woo; Lee, Joon Hyun

1999-01-01

A phased array is a multi-element piezoelectric device whose elements are individually excited by electric pulses at programmed delay time. One of the advantages of using phased array in nondestructive evaluation (NDE) application over conventional ultrasonic transducers is their great maneuverability of ultrasonic beam. There are some parameters such as the number and the size of the piezoelectric elements and the inter-element spacing of the elements to design phased array transducer. In this study, the characteristic of ultrasonic beam for phased array transducer due to the variation of the number of elements has been simulated for ultrasonic SH-wave on the basis of Huygen's principle. Ultrasonic beam directivity and focusing due to the change of time delay of each element were discussed due to the change of the number of piezoelectric elements. It was found that ultrasonic beam was much more spreaded and hence its sound pressure was decreased as steering angle of ultrasonic beam was increased. In addition, the ability of ultrasonic bean focusing decreased gradually with the increase of focal length at the same piezoelectric elements. However, the ability of beam focusing was improved as the number of consisting elements was increased

Gaussian vs. Bessel light-sheets: performance analysis in live large sample imaging

Science.gov (United States)

Reidt, Sascha L.; Correia, Ricardo B. C.; Donnachie, Mark; Weijer, Cornelis J.; MacDonald, Michael P.

2017-08-01

Lightsheet fluorescence microscopy (LSFM) has rapidly progressed in the past decade from an emerging technology into an established methodology. This progress has largely been driven by its suitability to developmental biology, where it is able to give excellent spatial-temporal resolution over relatively large fields of view with good contrast and low phototoxicity. In many respects it is superseding confocal microscopy. However, it is no magic bullet and still struggles to image deeply in more highly scattering samples. Many solutions to this challenge have been presented, including, Airy and Bessel illumination, 2-photon operation and deconvolution techniques. In this work, we show a comparison between a simple but effective Gaussian beam illumination and Bessel illumination for imaging in chicken embryos. Whilst Bessel illumination is shown to be of benefit when a greater depth of field is required, it is not possible to see any benefits for imaging into the highly scattering tissue of the chick embryo.

Conversion of isotropic fluorescence into a long-range non-diverging beam

Science.gov (United States)

Zhang, Douguo; Zhu, Liangfu; Chen, Junxue; Wang, Ruxue; Wang, Pei; Ming, Hai; Badugu, Ramachandram; Rosenfeld, Mary; Zhan, Qiwen; Kuang, Cuifang; Liu, Xu; Lakowicz, Joseph R.

2018-04-01

Fluorescent samples typically emit isotropically in all directions. Large lenses and other optical components are needed to capture a significant fraction of the emission, and complex confocal microscopes are required for high resolution focal-plane imaging. It is known that Bessel beams have remarkable properties of being able to travel over long distances, over 1000 times the wavelength, without diverging, and hence are called non-diffracting beams. In previous reports the Bessel beams were formed by an incident light source, typically with plane-wave illumination on a circular aperture. It was not known if Bessel beams could form from fluorescent light sources. We demonstrate transformation of the emission from fluorescent polystyrene spheres (FPS) into non-diverging beams which propagate up to 130 mm (13 cm) along the optical axis with a constant diameter. This is accomplished using a planar metal film, with no nanoscale features in the X-Y plane, using surface plasmon-coupled emission. Using samples which contain many FPS in the field-of-view, we demonstrate that an independent Bessel beam can be generated from any location on the metal film. The extremely long non-diffracted propagation distances, and self-healing properties of Bessel beams, offer new opportunities in fluorescence sensing and imaging.

Bessel functions: parallel display and processing.

Science.gov (United States)

Lohmann, A W; Ojeda-Castañeda, J; Serrano-Heredia, A

1994-01-01

We present an optical setup that converts planar binary curves into two-dimensional amplitude distributions, which are proportional, along one axis, to the Bessel function of order n, whereas along the other axis the order n increases. This Bessel displayer can be used for parallel Bessel transformation of a signal. Experimental verifications are included.

Choice of primary transducers of beam parameters for measuring and control systems of charged particle accelerators

International Nuclear Information System (INIS)

Rybin, V.M.

1981-01-01

Investigations on classification of primary transducers (pT) of the main parameters of charged particle beams are conducted for development of the common series on the base of program- controlled module systems for measuring the parameters of charged particle beams. The PT classification is exercised by: the physical principle of single transformation, the degree of effect on the beam, principle of operation, design, performance, location. It is shown that the optimal choice of PT and their parameters should be necessarily executed in several stages: estimation of the limiting possibilities of PT; choice of PT by time and metrological characteristics as well as sensitivity for the determined operation conditions; choice of the PT by the degree of effect on the beam: choice of the PT type with account of its design performance and location, determination of PT parameters with account of possibility of information, energy and design compatibility of the used standard. The classification results of magnetoinduction and acoustic transducers have shown that the number of their modifications does not exceed 100 [ru

Characterisation and Modelling of MEMS Ultrasonic Transducers

International Nuclear Information System (INIS)

Teng, M F; Hariz, A J

2006-01-01

Silicon ultrasonic transducer micro arrays based on micro-electro-mechanicalsystem (MEMS) technologies are gaining popularity for applications in sonar sensing and excitation. A current challenge for many researchers is modelling the dynamic performance of these and other micro-mechanical devices to ascertain their performance and explain experimental observations reported. In this work, the performance simulation of a MEMS ultrasonic transducer array made from silicon nitride has been successfully carried out using CoventorWare package. The dynamic response of the entire transducer array was characterised, and the results were compared with theoretical predictions. Individual elements were found to vibrate with Bessel-like displacement patterns, and they were resonant at approximately 3 MHz, depending on thickness and lateral dimensions. The frequency shows a linear dependence around the common thickness of 2 μm. Peak displacement levels were examined as a function of frequency, DC bias voltage, and AC drive voltage. Accounting for fabrication variations, and uniformity variations across the wafer, the full array showed minimal variations in peak out-of-plane displacement levels across the device, and isolated elements that were over-responsive and under-responsive. Presently, the effect of observed variations across the array on the performance of the transducers and their radiated fields are being examined

Beams made of twisted atoms: A theoretical analysis

Energy Technology Data Exchange (ETDEWEB)

Hayrapetyan, Armen [Physikalisches Institut, Ruprecht-Karls-Universitaet Heidelberg, 69120 Heidelberg (Germany); Matula, Oliver [Physikalisches Institut, Ruprecht-Karls-Universitaet Heidelberg, 69120 Heidelberg (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung, 64291 Darmstadt (Germany); Surzhykov, Andrey [Helmholtz-Institut Jena, 07743 Jena (Germany); Fritzsche, Stephan [Helmholtz-Institut Jena, 07743 Jena (Germany); Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitaet Jena, 07743 Jena (Germany)

2014-07-01

We have analyzed Bessel beams of two-level atoms that are driven by a linearly polarized laser light. Based on the Schroedinger equation for two-level systems, we first determine the states of two-level atoms in a plane-wave field by taking into account propagation directions both of the atom and the field. For such laser-driven two-level atoms, we construct Bessel beams by going beyond the typical paraxial approximation. In particular, we show that the probability density of these atomic beams exhibits a non-trivial, Bessel-squared-type behavior. The profile of such twisted atoms is affected by atom and laser parameters, such as the nuclear charge, atom velocity, laser frequency, and propagation geometry of the atom and laser beams. Moreover, we spatially and temporally characterize the beam of hydrogen and selected (neutral) alkali-metal atoms that carry non-zero orbital angular momentum (OAM). The proposed spatiotemporal Bessel states (i) are able to describe twisted states of any two-level system which is driven by the radiation field and (ii) have potential applications in atomic and nuclear processes as well as in quantum communication.

Harmonic Analysis Associated with the Generalized q-Bessel Operator

Directory of Open Access Journals (Sweden)

Ahmed Abouelaz

2016-01-01

Full Text Available In this article, we give a new harmonic analysis associated with the generalized q-Bessel operator. We introduce the generalized $q$-Bessel transform, the generalized q-Bessel translation and the generalized $q$-Bessel convolution product.

Transmission characteristics of Bessel-Gaussian vortex beams propagating along both longitudinal and transverse directions in a subway tunnel

Science.gov (United States)

Wang, Xiaohui; Song, Yingxiong

2018-02-01

By exploiting the non-Kolmogorov model and Rytov approximation theory, a propagation model of Bessel-Gaussian vortex beams (BGVB) propagating in a subway tunnel is derived. Based on the propagation model, a model of orbital angular momentum (OAM) mode probability distribution is established to evaluate the propagation performance when the beam propagates along both longitudinal and transverse directions in the subway tunnel. By numerical simulations and experimental verifications, the influences of the various parameters of BGVB and turbulence on the OAM mode probability distribution are evaluated, and the results of simulations are consistent with the experimental statistics. The results verify that the middle area of turbulence is more beneficial for the vortex beam propagation than the edge; when the BGVB propagates along the longitudinal direction in the subway tunnel, the effects of turbulence on the OAM mode probability distribution can be decreased by selecting a larger anisotropy parameter, smaller coherence length, larger non-Kolmogorov power spectrum coefficient, smaller topological charge number, deeper subway tunnel, lower train speed, and longer wavelength. When the BGVB propagates along the transverse direction, the influences can be also mitigated by adopting a larger topological charge number, less non-Kolmogorov power spectrum coefficient, smaller refractive structure index, shorter wavelength, and shorter propagation distance.

An adjustable multi-scale single beam acoustic tweezers based on ultrahigh frequency ultrasonic transducer.

Science.gov (United States)

Chen, Xiaoyang; Lam, Kwok Ho; Chen, Ruimin; Chen, Zeyu; Yu, Ping; Chen, Zhongping; Shung, K Kirk; Zhou, Qifa

2017-11-01

This paper reports the fabrication, characterization, and microparticle manipulation capability of an adjustable multi-scale single beam acoustic tweezers (SBAT) that is capable of flexibly changing the size of "tweezers" like ordinary metal tweezers with a single-element ultrahigh frequency (UHF) ultrasonic transducer. The measured resonant frequency of the developed transducer at 526 MHz is the highest frequency of piezoelectric single crystal based ultrasonic transducers ever reported. This focused UHF ultrasonic transducer exhibits a wide bandwidth (95.5% at -10 dB) due to high attenuation of high-frequency ultrasound wave, which allows the SBAT effectively excite with a wide range of excitation frequency from 150 to 400 MHz by using the "piezoelectric actuator" model. Through controlling the excitation frequency, the wavelength of ultrasound emitted from the SBAT can be changed to selectively manipulate a single microparticle of different sizes (3-100 μm) by using only one transducer. This concept of flexibly changing "tweezers" size is firstly introduced into the study of SBAT. At the same time, it was found that this incident ultrasound wavelength play an important role in lateral trapping and manipulation for microparticle of different sizes. Biotechnol. Bioeng. 2017;114: 2637-2647. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Characteristics of Far Transported Laser Beam

Energy Technology Data Exchange (ETDEWEB)

Park, Dae Yoon; Kim, Ki Sik; Lee, Seung Gol [Inha University, Inchon (Korea, Republic of)

1997-07-01

A beam propagating in free space or in a medium generally experiences diffraction, and hence it suffers an energy loss and an wavefront distortion. It Is essential for a stable and precise communication to eliminate or to minimize the diffraction effect accompanying on propagation. The diffraction-free beam is introduced for that purpose. A typical diffraction-free beam is the Bessel beam. The Bessel beam has, however, an infinite energy in the cross-section perpendicular to the direction of propagation and, because of this fact, its realizability is sceptical. To remedy this problem, a new beam is introduced, which has a series from with a Gaussian envelope function and tested for diffraction on propagation by a computer simulation. Compared with the Bessel-Gauss beam, this new beam shows much less diffraction. While, by using a scraper mirror in an Nd:YAG laser with a ring resonator, an annular output beam is obtained. This annular beam is focused by a Fourier Transformation lens to produce a diffraction-free beam. This diffraction-free beam dose not show any noticible diffraction on propagation over the distance of 16 m, which is determined by the scraper mirror and the Fourier transformation lens. This achievement provides a profound basis for the generation of diffraction-free beams over much longer distances. The developed technique will provide a stable and precise communication method in remote controlling system, remote sensing through atmosphere, and information transfer using the optical fiber. 30 refs., 22 figs. (author)

Acoustic radiation force on an air bubble and soft fluid spheres in ideal liquids: example of a high-order Bessel beam of quasi-standing waves.

Science.gov (United States)

Mitri, F G

2009-04-01

The partial wave series for the scattering of a high-order Bessel beam (HOBB) of acoustic quasi-standing waves by an air bubble and fluid spheres immersed in water and centered on the axis of the beam is applied to the calculation of the acoustic radiation force. A HOBB refers to a type of beam having an axial amplitude null and an azimuthal phase gradient. Radiation force examples obtained through numerical evaluation of the radiation force function are computed for an air bubble, a hexane, a red blood and mercury fluid spheres in water. The examples were selected to illustrate conditions having progressive, standing and quasi-standing waves with appropriate selection of the waves' amplitude ratio. An especially noteworthy result is the lack of a specific vibrational mode contribution to the radiation force determined by appropriate selection of the HOBB parameters.

BESSEL FILTER AND CHAOS: THREE-IN-ONE ACTION

DEFF Research Database (Denmark)

Tamaševicius, Arunas; Mykolaitis, Gytis; Bumeliene, Skaidra

2006-01-01

Low-pass active Bessel filters are proposed to be used in a chaotic oscillator. The Bessel unit plays the role of three-in-one: the delay line, the amplifier, and the filter. Results of Spice simulations and hardware experiments are presented.......Low-pass active Bessel filters are proposed to be used in a chaotic oscillator. The Bessel unit plays the role of three-in-one: the delay line, the amplifier, and the filter. Results of Spice simulations and hardware experiments are presented....

Extension of the beam theory for polymer bio-transducers with low aspect ratios and viscoelastic characteristics

International Nuclear Information System (INIS)

Du, Ping; Lin, I-Kuan; Zhang, Xin; Lu, Hongbing

2010-01-01

Polydimethylsiloxane (PDMS)-based micropillars (or microcantilevers) have been used as bio-transducers for measuring cellular forces on the order of pN to µN. The measurement accuracy of these sensitive devices depends on appropriate modeling to convert the micropillar deformations into the corresponding reaction forces. The traditional approach to calculating the reaction force is based on the Euler beam theory with consideration of a linear elastic slender beam for the micropillar. However, the low aspect ratio in geometry of PDMS micropillars does not satisfy the slender beam requirement. Consequently, the Timoshenko beam theory, appropriate for a beam with a low aspect ratio, should be used. In addition, the inherently time-dependent behavior in PDMS has to be considered for accurate force conversion. In this paper, the Timoshenko beam theory, along with the consideration of viscoelastic behavior of PDMS, was used to model the mechanical response of micropillars. The viscoelastic behavior of PDMS was characterized by stress relaxation nanoindentation using a circular flat punch. A correction procedure was developed to determine the load–displacement relationship with consideration of ramp loading. The relaxation function was extracted and described by a generalized Maxwell model. The bending of rectangular micropillars was performed by a wedge indenter tip. The viscoelastic Timoshenko beam formula was used to calculate the mechanical response of the micropillar, and the results were compared with measurement data. The calculated reaction forces agreed well with the experimental data at three different loading rates. A parametric study was conducted to evaluate the accuracy of the viscoelastic Timoshenko beam model by comparing the reaction forces calculated from the elastic Euler beam, elastic Timoshenko beam and viscoelastic Euler beam models at various aspect ratios and loading rates. The extension of modeling from the elastic Euler beam theory to the

A Determinant Expression for the Generalized Bessel Polynomials

Directory of Open Access Journals (Sweden)

Sheng-liang Yang

2013-01-01

Full Text Available Using the exponential Riordan arrays, we show that a variation of the generalized Bessel polynomial sequence is of Sheffer type, and we obtain a determinant formula for the generalized Bessel polynomials. As a result, the Bessel polynomial is represented as determinant the entries of which involve Catalan numbers.

Excitation of multipolar surface plasmon resonance in plasmonic nanoparticles by complex accelerating beams

Science.gov (United States)

Yang, Yang; Li, Jiafang; Li, Zhi-Yuan; Chen, Yue-Gang

2015-07-01

In this paper, through a vector-spherical harmonics approach, we investigate the optical spectra of plasmonic Au nanoparticles excited by two special accelerating beams: a non-paraxial Airy beam and a Bessel beam. We systematically analyze the impacts of the beam profile, phase, and helical wave front of the electromagnetic fields on the optical spectrum and the excitation of the surface plasmon resonance (SPR). We find that the high-order phase in the Airy beam would result in strong plasmonic oscillations in the optical spectra, while the cone angle and orbital angular momentum carried by the Bessel beam could be employed to engineer the plasmon modes excited in Au nanoparticles. Furthermore, the optical spectrum excited by a combined Airy-Bessel-Gauss beam is discussed. The study could help to deeply explore new ways to manipulate SPR in metal nanoparticles via the wave front engineering of optical beams for enhancing light-matter interaction and optical sensing performance.

Topological setting of Bessel functions

International Nuclear Information System (INIS)

Mekhfi, M.

1995-11-01

We start from the topology of the punctured plane encoded within its homotopy group which is isomorphic to the set of integers Z. We then realize group elements Π(n), n is an element of Z as differential operators on the space of analytic functions. Using plausible physical arguments we select a subset of functions which we identify with integer orders reduced Bessel functions. On the other hand we propose a unifying new formula of topological origin, generating real orders Bessel functions out of integers orders ones, the generator being an operator built entirely out of the Π s . We thus have shown that the topology (of the puntured plane) is underlying the inner structure of Bessel functions, in addition it unifies them independently of the orders being integers or reals. (author). 4 refs

Extension of Oppenheim's Problem to Bessel Functions

Directory of Open Access Journals (Sweden)

Zhu Ling

2007-01-01

Full Text Available Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we deduce the hyperbolic analogue of these trigonometric inequalities, and we extend these inequalities to modified Bessel functions.

Modified Bessel P-integrals and P-derivatives and their properties

International Nuclear Information System (INIS)

Volosivets, S S

2014-01-01

We study the modified Bessel P-integral, whose properties are similar to those of the Bessel potential, and the modified Bessel P-derivative. These operators are inverse to each other. We prove analogues of the embedding theorems of Hardy, Littlewood, Stein, Zygmund and Lizorkin concerning the images of L p (R) under the action of Bessel potentials. We give applications of the Bessel integral and derivative to the integrability of the P-adic Fourier transform and to approximation theory (an embedding theorem of Ul'yanov type)

DEVELOPMENTAL STUDIES OF NUCLEAR DIGITAL TRANSDUCERS

Energy Technology Data Exchange (ETDEWEB)

Hyde, James L.

1963-09-15

A pressure transducer based on mechanical modulation of a beam of alpha particles is described. This type of transducer is capable of direct digital pressure measurexnent with corresponding telemetry advantages. Any variable that is sensed through a mechanical displacement is measurable by means of a corresponding member of this transducer family. Preliminary tests of an experimental pressure transducer show an overall accuracy within a few tenths of one percent, with promise of substantial improvement. General characteristics of nuclear digital transducers include exceptional long-term calibration stability and accuracy, independent of ambient environmental effects. Three concepts of systems enipioying these transducers are discussed. (auth)

Sobre la inversión de los potenciales de Bessel-Riesz Sobre la inversión de los potenciales de Bessel-Riesz

Directory of Open Access Journals (Sweden)

Ruben Alejandro Cerutti

2010-02-01

Full Text Available En este trabajo se obtiene la inversión de un operador del tipo convolución usando técnicas de integrales hipersingulares. El operador de Bessel-Riesz de una función ϕ perteneciente a S , el espacio de funciones de prueba de Schwartz, es definido por la convolución con las funciones generalizadas (fórmula expresables en términos de la función de Bessel de primera especie (formula es también una combinación lineal infinita del núcleo ultrahiperbólico de Riesz de diferentes ordenes. Este hecho nos permite invertir los potenciales de Bessel-Riesz de un modo análogo a lo αhecho en el caso de los potenciales ultrahiperbólicos de Bessel (cf. [01] y los potenciales causales de Riesz (cf. [2].In this paper the inversion of a convolution type operator is obtained by using hypersingular integral technics. The Bessel-Riesz operator of a function ϕ belonging to S , the space of test functions of Schwartz, is definied by the convolution with the generalized functions  (formula expressible in terms of the Bessel function of first kind (formula . γ is also an infinite linear combination of the ultrahyperbolic Riesz kernel of differents orders. This fact allows us to invert the Bessel-Riesz potential in an analogue manner of the ultrahyperbolic Bessel potentials (cf. [01] and causal Riesz potentials (cf. [2].

Self-reconstruction of diffraction-free and accelerating laser beams in scattering media

International Nuclear Information System (INIS)

Ersoy, T.; Yalizay, B.; Akturk, S.

2012-01-01

We experimentally investigate propagation of laser beams with different intensity profiles in highly scattering media. We generate transverse laser amplitude profiles with Gaussian, Bessel and Airy function envelopes. We then propagate these beams through optical phantoms formed with variable density intralipid solutions. At the sample exit, we compare change in maximum intensities, as well as beam profile reconstruction. We show that self-reconstruction properties of Bessel and Airy beams bring about slower decrease in maximum intensity with increasing scatterer density. On the other hand, the beam profiles deteriorate faster, as compared to reference Gaussian beams. Slower decrease in the intensity can be attributed to the wavevector spectra providing a continuous flow of energy to the beam center, while beam deterioration is linked to total beam volume in the scattering medium. These results show that beam shaping methods can significantly enhance delivery of intense light deeper into turbid media, but this enhancement is compromised by stronger speckling of beam profiles. -- Highlights: ► We experimentally investigate propagation of shaped laser beams in turbid media. ► Peak intensity of Bessel and Airy beams decrease slower with increasing scatterer. ► Shaped beam profiles deteriorate faster, as compared to reference Gaussian beams. ► Shaped beam profiles can enhance applications of lasers inscattering media.

Zernike vs. Bessel circular functions in visual optics.

Science.gov (United States)

Trevino, Juan P; Gómez-Correa, Jesus E; Iskander, D Robert; Chávez-Cerda, Sabino

2013-07-01

We propose the Bessel Circular Functions as alternatives of the Zernike Circle Polynomials to represent relevant circular ophthalmic surfaces. We assess the fitting capabilities of the orthogonal Bessel Circular Functions by comparing them to Zernike Circle Polynomials for approximating a variety of computationally generated surfaces which can represent ophthalmic surfaces. The Bessel Circular Functions showed better modelling capabilities for surfaces with abrupt variations such as the anterior eye surface at the limbus region, and influence functions. From our studies we find that the Bessel Circular Functions can be more suitable for studying particular features of post surgical corneal surfaces. We show that given their boundary conditions and free oscillating properties, the Bessel Circular Functions are an alternative for representing specific wavefronts and can be better than the Zernike Circle Polynomials for some important cases of corneal surfaces, influence functions and the complete anterior corneal surface. © 2013 The Authors Ophthalmic & Physiological Optics © 2013 The College of Optometrists.

Generalized approach to modifying optical vortices with suppressed sidelobes using Bessel-like functions.

Science.gov (United States)

Chen, J; Yuan, X-C; Zhao, X; Fang, Z L; Zhu, S W

2009-11-01

We propose a generalized approach to producing optical vortices with suppressed sidelobes using a variable Bessel-like function added to the conventional spiral phase plate. Experimental verifications are implemented by a phase-only spatial light modulator. It is demonstrated that the method is valid for optical vortex beams with arbitrary topological charges and without changing the primary ring size as a unique property among the existing techniques.

Computation of hyperspherical Bessel functions

OpenAIRE

Tram, Thomas

2013-01-01

In this paper we present a fast and accurate numerical algorithm for the computation of hyperspherical Bessel functions of large order and real arguments. For the hyperspherical Bessel functions of closed type, no stable algorithm existed so far due to the lack of a backwards recurrence. We solved this problem by establishing a relation to Gegenbauer polynomials. All our algorithms are written in C and are publicly available at Github [https://github.com/lesgourg/class_public]. A Python wrapp...

Theory of generalized Bessel functions

International Nuclear Information System (INIS)

Dattoli, G.; Giannessi, L.; Mezi, L.; Torre, A.

1990-01-01

In this paper it is discussed the theory of generalized Bessel functions which are of noticeable importance in the analysis of scattering processes for which the dipole approximation cannot be used. These functions have been introduced in their standard form and their modified version. The relevant generating functions and Graf-type addition theorems have been stated. The usefulness of the results to construct a fast algorithm for their quantitative computation is also devised. It is commented on the possibility of getting two-index generalized Bessel functions in e.g. the study of sum rules of the type Σ n=-∞ ∞ t n J n 3 (x), where J n is the cylindrical Bessel function of the first kind. The usefulness of the results for problems of practical interest is finally commented on. It is shown that a modified Anger function can be advantageously introduced to get an almost straightforward computation of the Bernstein sum rule in the theory of ion waves

Generating bessel functions in mie scattering calculations using continued fractions.

Science.gov (United States)

Lentz, W J

1976-03-01

A new method of generating the Bessel functions and ratios of Bessel functions necessary for Mie calculations is presented. Accuracy is improved while eliminating the need for extended precision word lengths or large storage capability. The algorithm uses a new technique of evaluating continued fractions that starts at the beginning rather than the tail and has a built-in error check. The continued fraction representations for both spherical Bessel functions and ratios of Bessel functions of consecutive order are presented.

FUNPACK-2, Subroutine Library, Bessel Function, Elliptical Integrals, Min-max Approximation

International Nuclear Information System (INIS)

Cody, W.J.; Garbow, Burton S.

1975-01-01

1 - Description of problem or function: FUNPACK is a collection of FORTRAN subroutines to evaluate certain special functions. The individual subroutines are (Identification/Description): NATSI0 F2I0 Bessel function I 0 ; NATSI1 F2I1 Bessel function I 1 ; NATSJ0 F2J0 Bessel function J 0 ; NATSJ1 F2J1 Bessel function J 1 ; NATSK0 F2K0 Bessel function K 0 ; NATSK1 F2K1 Bessel function K 1 ; NATSBESY F2BY Bessel function Y ν ; DAW F1DW Dawson's integral; DELIPK F1EK Complete elliptic integral of the first kind; DELIPE F1EE Complete elliptic integral of the second kind; DEI F1EI Exponential integrals; NATSPSI F2PS Psi (logarithmic derivative of gamma function); MONERR F1MO Error monitoring package . 2 - Method of solution: FUNPACK uses evaluation of min-max approximations

Model of a Piezoelectric Transducer

Science.gov (United States)

Goodenow, Debra

2004-01-01

It's difficult to control liquid and gas in propellant tanks in zero gravity. A possible a design would utilize acoustic liquid manipulation (ALM) technology which uses ultrasonic beams conducted through a liquid and solid media, to push gas bubbles in the liquid to desirable locations. We can propel and control the bubble with acoustic radiation pressure by aiming the acoustic waves on the bubble s surface. This allows us to design a so called smart tank in which the ALM devices transfer the gas to the outer wall of the tank and isolating the liquid in the center. Because the heat transfer rate of a gas is lower of that of the liquid it would substantially decrease boil off and provide of for a longer storage life. The ALM beam is composed of little wavelets which are individual waves that constructively interfere with each other to produce a single, combined acoustic wave front. This is accomplished by using a set of synchronized ultrasound transducers arranged in an array. A slight phase offset of these elements allows us to focus and steer the beam. The device that we are using to produce the acoustic beam is called the piezoelectric transducer. This device converts electrical energy to mechanical energy, which appears in the form of acoustic energy. Therefore the behavior of the device is dependent on both the mechanical characteristics, such as its density, cross-sectional area, and its electrical characteristics, such as, electric flux permittivity and coupling factor. These devices can also be set up in a number of modes which are determined by the way the piezoelectric device is arranged, and the shape of the transducer. For this application we are using the longitudinal or thickness mode for our operation. The transducer also vibrates in the lateral mode, and one of the goals of my project is to decrease the amount of energy lost to the lateral mode. To model the behavior of the transducers I will be using Pspice, electric circuit modeling tool, to

Improved passive shunt vibration control of smart piezo-elastic beams using modal piezoelectric transducers with shaped electrodes

International Nuclear Information System (INIS)

Vasques, C M A

2012-01-01

Modal control and spatial filtering technologies for mitigation of vibration and/or structural acoustics radiation may be achieved through the use of distributed modal piezoelectric transducers with properly shaped electrodes. This approach filters out undesirable and uncontrollable modes over the bandwidth of interest in order to increase the robustness and stability of the controlled structural system, and may also yield higher values of the generalized modal electromechanical coupling coefficient, which is an important design parameter for achieving efficient passive shunt damping design. In this paper the improvements in passive shunt damping performance when using modal piezoelectric transducers with shaped electrodes are investigated for a two-layered resonant-shunted piezo-elastic smart beam structure. An electromechanical one-dimensional equivalent single-layer Euler–Bernoulli analytical model of two-layered smart piezo-elastic beams with arbitrary spatially shaped electrodes is established for modal and uniform electrode designs. The model is verified and validated by comparison with a one-dimensional discrete-layer (layerwise) finite element model, the damping performance of the shunted smart beam with shaped electrodes is investigated and assessed in terms of the generalized electromechanical coupling coefficient and frequency responses obtained when considering uniform and modally shaped electrodes and the underlying improved performance and advantages are assessed and discussed. (paper)

The Bessel polynomials and their differential operators

International Nuclear Information System (INIS)

Onyango Otieno, V.P.

1987-10-01

Differential operators associated with the ordinary and the generalized Bessel polynomials are defined. In each case the commutator bracket is constructed and shows that the differential operators associated with the Bessel polynomials and their generalized form are not commutative. Some applications of these operators to linear differential equations are also discussed. (author). 4 refs

Poisson processes and a Bessel function integral

NARCIS (Netherlands)

Steutel, F.W.

1985-01-01

The probability of winning a simple game of competing Poisson processes turns out to be equal to the well-known Bessel function integral J(x, y) (cf. Y. L. Luke, Integrals of Bessel Functions, McGraw-Hill, New York, 1962). Several properties of J, some of which seem to be new, follow quite easily

All-optical 3D atomic loops generated with Bessel light fields

International Nuclear Information System (INIS)

Volke-Sepulveda, Karen; Jauregui, RocIo

2009-01-01

The propagation invariance of Bessel beams as well as their transversal structure is used to perform a comparative analysis of their effect on cold atoms for four different configurations and combinations thereof. We show that, even at temperatures for which the classical description of the atom's centre-of-mass motion is valid, the interchange of momentum, energy and orbital angular momentum between light and atoms yields efficient tools for all-optical trapping, transporting and, in general, manipulating the state of motion of cold atoms.

A line scanned light-sheet microscope with phase shaped self-reconstructing beams.

Science.gov (United States)

Fahrbach, Florian O; Rohrbach, Alexander

2010-11-08

We recently demonstrated that Microscopy with Self-Reconstructing Beams (MISERB) increases both image quality and penetration depth of illumination beams in strongly scattering media. Based on the concept of line scanned light-sheet microscopy, we present an add-on module to a standard inverted microscope using a scanned beam that is shaped in phase and amplitude by a spatial light modulator. We explain technical details of the setup as well as of the holograms for the creation, positioning and scaling of static light-sheets, Gaussian beams and Bessel beams. The comparison of images from identical sample areas illuminated by different beams allows a precise assessment of the interconnection between beam shape and image quality. The superior propagation ability of Bessel beams through inhomogeneous media is demonstrated by measurements on various scattering media.

Series of Bessel and Kummer-type functions

CERN Document Server

Baricz, Arpad; Pogány, Tibor K

2017-01-01

This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the series of Bessel functions considered. Some integral representations are deduced using techniques from the theory of differential equations. The text is aimed at a mathematical audience, including graduate students and those in the scientific community who are interested in a new perspective on Fourier–Bessel series, and their manifold and polyvalent applications, mainly in general classical analysis, applied mathematics and mathematical physics.

Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials

International Nuclear Information System (INIS)

Doha, E H; Ahmed, H M

2004-01-01

A formula expressing explicitly the derivatives of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another explicit formula, which expresses the Bessel expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of its original Bessel coefficients, is also given. A formula for the Bessel coefficients of the moments of one single Bessel polynomial of certain degree is proved. A formula for the Bessel coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Bessel coefficients is also obtained. Application of these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Bessel-Bessel polynomials is described. An explicit formula for these coefficients between Jacobi and Bessel polynomials is given, of which the ultraspherical polynomial and its consequences are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Bessel and Hermite-Bessel are also developed

Semi-Inclusive Deep Inelastic Scattering and Bessel-Weighted Asymmetries

International Nuclear Information System (INIS)

Gamberg, Leonard; Boer, Daniel; Musch, Bernhard; Prokudin, Alexei

2012-01-01

We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel-weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.

Higher-order chaotic oscillator using active bessel filter

DEFF Research Database (Denmark)

Lindberg, Erik; Mykolaitis, Gytis; Bumelien, Skaidra

2010-01-01

A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel filter is described. The Bessel unit plays the role of "three-in-one": a delay line, an amplifier and a filter. Results of hardware experiments and numerical simulation are presented. Depending...

Generalized Bessel functions in tunnelling ionization

International Nuclear Information System (INIS)

Reiss, H R; Krainov, V P

2003-01-01

We develop two new approximations for the generalized Bessel function that frequently arises in the analytical treatment of strong-field processes, especially in non-perturbative multiphoton ionization theories. Both these new forms are applicable to the tunnelling environment in atomic ionization, and are analytically much simpler than the currently used low-frequency asymptotic approximation for the generalized Bessel function. The second of the new forms is an approximation to the first, and it is the second new form that exhibits the well-known tunnelling exponential

Bessel functions for root systems via the trigonometric setting

DEFF Research Database (Denmark)

Ørsted, Bent; Said, S.B.

2005-01-01

In this paper, we study generalized Bessel functions related to root systems and give explicit formulas in several cases.......In this paper, we study generalized Bessel functions related to root systems and give explicit formulas in several cases....

Bessel-Weighted Asymmetries in Semi Inclusive Deep Inelastic Scattering

International Nuclear Information System (INIS)

Boer, D.; Gamberg, L.; Musch, B.U.; Prokudin, A.

2011-01-01

The concept of weighted asymmetries is revisited for semi-inclusive deep inelastic scattering. We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.

Generating and analyzing non-diffracting vector vortex beams

CSIR Research Space (South Africa)

Li, Y

2013-08-01

Full Text Available single order Bessel beam and superposition cases are studied. The polarization and the azimuthal modes of the generated beams are analyzed. The results of modal decompositions on polarization components are in good agreement with theory. We demonstrate...

Control of the ultrasonic beam transmitted through an irregular profile using a smart flexible transducer: modelling an application

Energy Technology Data Exchange (ETDEWEB)

Roy, O.; Mahaut, S.; Casula, O. [CEA Fontenay aux Roses, DRT/LIST/DECS/STA/LMUS, 92 (France)

2001-07-01

In most of industries as aeronautics, aerospace and nuclear, the main part of the ultrasonic testing is carried out directly in touch with the inspected component. Among others, the cooling piping of French pressurized water reactor comprises many welding components with complex geometry: elbows, butt welds, nozzles. In service inspections of such components performed with conventional ultrasonic contact transducers present limited performances. Variations in sensitivity are produced by unmatched contact on irregular surface, which results in poor detection performances. In addition, the beam orientation transmitted through complex interfaces cannot be totally controlled, because of the disorientations suffered by the transducer during its displacement. As a result, a possible defect cannot be correctly detected, positioned and characterized. At last, the geometry of some components limits the displacement of the transducer, resulting in an uncovered scan area. To overcome these difficulties and to improve the performances of such inspections, the CEA, supported by the safety authorities (IPSN), has developed a new concept of phased array. Recent studies have been made to obtain further performances improvements of this system, including instrumentation development and a new phased array design. Inspections have been performed on a specimen containing artificial defects under a realistic profile, with an adaptive mode to compensate the effect of the irregular profile. Experimental results, displayed using specific imaging, show the ability of this system to detect and characterize defects under irregular profiles, using longitudinal or shear waves in a fully mastered beam. (authors)

The Bessel functions J0 and J1 of complex argument

International Nuclear Information System (INIS)

Ardill, R.W.B.; Moriarty, K.J.M.

1977-01-01

The Bessel function appears in a wide range of physical applications. The package Bessel contains complex function routines to calculate J 0 (z) and J 1 (z) for complex z. Bessel functions of higher order n 0 (z) and J 1 (z) for all values of mod(z) up to machine overflow. For mod(z) 10, the results diverge quite rapidly from their actual values. The accuracy for mod(z)<=10 is sufficient for most physical applications, and the polynomial approximations provide a quicker calculation of Bessel functions than the use of the ascending series formula used previously, particularly for values of mod(z) near 10. (Auth.)

Bessel-like beams with z-dependent cone angles

CSIR Research Space (South Africa)

Belyi, VN

2009-08-01

Full Text Available beams (keeping the transverse profile at any distances). This new type of beams can be obtained in optical system composed of lens axicon doublet and conical lens. An experimental set-up for producing such beams is realized. It is shown that depending...

Numerical comparison of patch and sandwich piezoelectric transducers for transmitting ultrasonic waves

CSIR Research Space (South Africa)

Loveday, PW

2006-03-01

Full Text Available in the waveguide. Piezoelectric patch transducers are frequently employed, by researchers, for exciting waves in beam like structures. Sonar systems frequently make use of resonant transducers, such as sandwich transducers, for acoustic wave generation...

Generation and propagation of high-order Bessel vortices in linear and non-linear crystals

CSIR Research Space (South Africa)

Belyi, VN

2009-08-01

Full Text Available E⊥ of the electric field for these beams are given by the following expressions: ( ))2exp()()( )( )exp( 20 1 10 ϕρρ iqJqJ qw zikA i zoo −+⊥ += eeE , (1) с Uniaxial crystal θs Bs2ω(ρ) Bsω(ρ) Figure 1: Geometry of SHG when wave vectors cone of Bessel... beam at fundamental )(ρωBs and second harmonic frequencies )(2 ρωBs coincides with phase-matching cone of uniaxial crystal. Proc. of SPIE Vol. 7430 74300F-2 ( ))2exp()()()cos( )( )exp( 20 1 1 ϕρργ iqJqJ qw zikA i e zee e −+⊥ −= ee...

Computer program for Bessel and Hankel functions

Science.gov (United States)

Kreider, Kevin L.; Saule, Arthur V.; Rice, Edward J.; Clark, Bruce J.

1991-01-01

A set of FORTRAN subroutines for calculating Bessel and Hankel functions is presented. The routines calculate Bessel and Hankel functions of the first and second kinds, as well as their derivatives, for wide ranges of integer order and real or complex argument in single or double precision. Depending on the order and argument, one of three evaluation methods is used: the power series definition, an Airy function expansion, or an asymptotic expansion. Routines to calculate Airy functions and their derivatives are also included.

Three-dimensional Bessel light bullets in self-focusing Kerr media

International Nuclear Information System (INIS)

Zhong Weiping; Belic, Milivoj; Huang Tingwen

2010-01-01

We study three-dimensional (3D) Bessel light-bullet solutions of the nonlinear Schroedinger equation with a photonic lattice potential in the form of squared Bessel functions in polar coordinates, both analytically and numerically. Analytical solutions are obtained by the Hartree approximation, and numerical simulations are performed, to compare with the analytical solutions and to confirm the stability of localized solutions. The 3D spatial wave packets are built by the products of hyperbolic secant and Bessel functions. These solitons appear in different forms, such as 3D vortex solitons and multipole solitons.

Bessel harmonic analysis and approximation of functions on the half-line

International Nuclear Information System (INIS)

Platonov, Sergei S

2007-01-01

We study problems of approximation of functions on [0,+∞) in the metric of L p with power weight using generalized Bessel shifts. We prove analogues of direct Jackson theorems for the modulus of smoothness of arbitrary order defined in terms of generalized Bessel shifts. We establish the equivalence of the modulus of smoothness and the K-functional. We define function spaces of Nikol'skii-Besov type and describe them in terms of best approximations. As a tool for approximation, we use a certain class of entire functions of exponential type. In this class, we prove analogues of Bernstein's inequality and others for the Bessel differential operator and its fractional powers. The main tool we use to solve these problems is Bessel harmonic analysis

Excitation of multipolar surface plasmon resonance in plasmonic nanoparticles by complex accelerating beams

International Nuclear Information System (INIS)

Yang, Yang; Li, Jiafang; Li, Zhi-Yuan; Chen, Yue-Gang

2015-01-01

In this paper, through a vector-spherical harmonics approach, we investigate the optical spectra of plasmonic Au nanoparticles excited by two special accelerating beams: a non-paraxial Airy beam and a Bessel beam. We systematically analyze the impacts of the beam profile, phase, and helical wave front of the electromagnetic fields on the optical spectrum and the excitation of the surface plasmon resonance (SPR). We find that the high-order phase in the Airy beam would result in strong plasmonic oscillations in the optical spectra, while the cone angle and orbital angular momentum carried by the Bessel beam could be employed to engineer the plasmon modes excited in Au nanoparticles. Furthermore, the optical spectrum excited by a combined Airy–Bessel–Gauss beam is discussed. The study could help to deeply explore new ways to manipulate SPR in metal nanoparticles via the wave front engineering of optical beams for enhancing light–matter interaction and optical sensing performance. (paper)

Ultrasonic field analysis program for transducer design in the nuclear industry

International Nuclear Information System (INIS)

Singh, G.P.; Rose, J.L.

1980-02-01

An ultrasonic field analysis program is presented that can be used for transducer design in the nuclear industry. Calculation routines that make use of Huygen's principle in a field analysis model are introduced that enable such field characteristics as axial and lateral resolution, beam symmetry, and gain variation throughout the ultrasonic field to be optimized. Mathematical details are presented along with several sample problems that show comparisons with classical results reported in the literature and with experimental data. Several sample problems that are of interest to the nuclear industry are also included, along with some that satisfy both academical and practical curiosity. These include transducer shape effects, pulse shape effects, crystal vibration variation, and an introduction to such novel transducer designs as annular arrays and dual element angle beam transducers

Application of a non-integer Bessel uniform approximation to inelastic molecular collisions

International Nuclear Information System (INIS)

Connor, J.N.L.; Mayne, H.R.

1979-01-01

A non-integer Bessel uniform approximation has been used to calculate transition probabilities for collinear atom-oscillator collisions. The collision systems used are a harmonic oscillator interacting via a Lennard-Jones potential and a Morse oscillator interacting via an exponential potential. Both classically allowed and classically forbidden transitions have been treated. The order of the Bessel function is chosen by a physical argument that makes use of information contained in the final-action initial-angle plot. Limitations of this procedure are discussed. It is shown that the non-integer Bessel approximation is accurate for elastic 0 → 0 collisions at high collision energies, where the integer Bessel approximation is inaccurate or inapplicable. (author)

Design of Extended Depth-of-Focus Laser Beams Using Orthogonal Beam Expansions

Directory of Open Access Journals (Sweden)

Leonard Bergstein

2005-06-01

Full Text Available Laser beams with extended depth of focus have many practical applications, such as scanning printed bar codes. Previous work has concentrated on synthesizing such beams by approximating the nondiffracting Bessel beam solution to the wave equation. In this paper, we introduce an alternate novel synthesis method that is based on maintaining a minimum MTF value (contrast over the largest possible distance. To achieve this, the coefficients of an orthogonal beam expansion are sequentially optimized to this criterion. One of the main advantages of this method is that it can be easily generalized to noncircularly symmetrical beams by the appropriate choice of the beam expansion basis functions. This approach is found to be very useful for applications that involve scanning of the laser beam.

q-Sumudu transforms of q-analogues of Bessel functions.

Science.gov (United States)

Uçar, Faruk

2014-01-01

The main purpose of this paper is to evaluate q-Sumudu transforms of a product of q-Bessel functions. Interesting special cases of theorems are also discussed. Further, the results proved in this paper may find certain applications of q-Sumudu transforms to the solutions of the q-integrodifferential equations involving q-Bessel functions. The results may help to extend the q-theory of orthogonal functions.

A Doubly-Curved Piezoelectric Composite with 1-3 Connectivity for Underwater Transducer Applications

Science.gov (United States)

Zhang, Yanjun; Wang, Likun; Qin, Lei; Liao, Qingwei; Zhong, Chao

2018-03-01

Aim to increase the horizontal and vertical beam width of the high frequency transducer simultaneously, we present a doubly-curved 1-3 piezoelectric composite element. It consists of 54% piezoelectric ceramic volume fraction and two phases polymer matrix. The finite element analysis (FEA) is used to evaluate the dynamic response of composite. Electroacoustic response in water was measured for the doubly-curved composite being considered as underwater transducer. An underwater transducer was fabricated using the doubly-curved 1-3 piezoelectric composite element. The -3 dB full angle beam width of transducer is approximately 106° and 36° in the horizontal and vertical plane respectively. Both the FEA simulations and experimental results show the potential of a broad covered area of the composite transducer in underwater environment.

Cylindrically polarized Bessel–Gauss beams

International Nuclear Information System (INIS)

Madhi, Daena; Aiello, Andrea; Ornigotti, Marco

2015-01-01

We present a study of radially and azimuthally polarized Bessel–Gauss (BG) beams in both the paraxial and nonparaxial regime. We discuss the validity of the paraxial approximation and the form of the nonparaxial corrections for BG beams. We show that independently on the ratio between the Bessel aperture cone angle ϑ 0 and the Gaussian beam divergence θ 0 , the nonparaxial corrections are alway very small and therefore negligible. The explicit expressions for the nonparaxial vector electric field components are also reported. (paper)

Approximation of Analytic Functions by Bessel's Functions of Fractional Order

Directory of Open Access Journals (Sweden)

Soon-Mo Jung

2011-01-01

Full Text Available We will solve the inhomogeneous Bessel's differential equation x2y″(x+xy′(x+(x2-ν2y(x=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.

Bessel collocation approach for approximate solutions of Hantavirus infection model

Directory of Open Access Journals (Sweden)

Suayip Yuzbasi

2017-11-01

Full Text Available In this study, a collocation method is introduced to find the approximate solutions of Hantavirus infection model which is a system of nonlinear ordinary differential equations. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. This method converts Hantavirus infection model into a matrix equation in terms of the Bessel functions of first kind, matrix operations and collocation points. The matrix equation corresponds to a system of nonlinear equations with the unknown Bessel coefficients. The reliability and efficiency of the suggested scheme are demonstrated by numerical applications and all numerical calculations have been done by using a program written in Maple.

Probing neural tissue with airy light-sheet microscopy: investigation of imaging performance at depth within turbid media

Science.gov (United States)

Nylk, Jonathan; McCluskey, Kaley; Aggarwal, Sanya; Tello, Javier A.; Dholakia, Kishan

2017-02-01

Light-sheet microscopy (LSM) has received great interest for fluorescent imaging applications in biomedicine as it facilitates three-dimensional visualisation of large sample volumes with high spatiotemporal resolution whilst minimising irradiation of, and photo-damage to the specimen. Despite these advantages, LSM can only visualize superficial layers of turbid tissues, such as mammalian neural tissue. Propagation-invariant light modes have played a key role in the development of high-resolution LSM techniques as they overcome the natural divergence of a Gaussian beam, enabling uniform and thin light-sheets over large distances. Most notably, Bessel and Airy beam-based light-sheet imaging modalities have been demonstrated. In the single-photon excitation regime and in lightly scattering specimens, Airy-LSM has given competitive performance with advanced Bessel-LSM techniques. Airy and Bessel beams share the property of self-healing, the ability of the beam to regenerate its transverse beam profile after propagation around an obstacle. Bessel-LSM techniques have been shown to increase the penetration-depth of the illumination into turbid specimens but this effect has been understudied in biologically relevant tissues, particularly for Airy beams. It is expected that Airy-LSM will give a similar enhancement over Gaussian-LSM. In this paper, we report on the comparison of Airy-LSM and Gaussian-LSM imaging modalities within cleared and non-cleared mouse brain tissue. In particular, we examine image quality versus tissue depth by quantitative spatial Fourier analysis of neural structures in virally transduced fluorescent tissue sections, showing a three-fold enhancement at 50 μm depth into non-cleared tissue with Airy-LSM. Complimentary analysis is performed by resolution measurements in bead-injected tissue sections.

K-Bessel functions associated to a 3-rank Jordan algebra

Directory of Open Access Journals (Sweden)

Hacen Dib

2005-01-01

Full Text Available Using the Bessel-Muirhead system, we can express the K-Bessel function defined on a Jordan algebra as a linear combination of the J-solutions. We determine explicitly the coefficients when the rank of this Jordan algebra is three after a reduction to the rank two. The main tools are some algebraic identities developed for this occasion.

Fourier expansions and multivariable Bessel functions concerning radiation programmes

International Nuclear Information System (INIS)

Dattoli, G.; Richetta, M.; Torre, A.; Chiccoli, C.; Lorenzutta, S.; Maino, G.

1996-01-01

The link between generalized Bessel functions and other special functions is investigated using the Fourier series and the generalized Jacobi-Anger expansion. A new class of multivariable Hermite polynomials is then introduced and their relevance to physical problems discussed. As an example of the power of the method, applied to radiation physics, we analyse the role played by multi-variable Bessel functions in the description of radiation emitted by a charge constrained to a nonlinear oscillation. (author)

Generalized theory of resonance excitation by sound scattering from an elastic spherical shell in a nonviscous fluid.

Science.gov (United States)

Mitri, Farid G

2012-08-01

This work presents the general theory of resonance scattering (GTRS) by an elastic spherical shell immersed in a nonviscous fluid and placed arbitrarily in an acoustic beam. The GTRS formulation is valid for a spherical shell of any size and material regardless of its location relative to the incident beam. It is shown here that the scattering coefficients derived for a spherical shell immersed in water and placed in an arbitrary beam equal those obtained for plane wave incidence. Numerical examples for an elastic shell placed in the field of acoustical Bessel beams of different types, namely, a zero-order Bessel beam and first-order Bessel vortex and trigonometric (nonvortex) beams are provided. The scattered pressure is expressed using a generalized partial-wave series expansion involving the beam-shape coefficients (BSCs), the scattering coefficients of the spherical shell, and the half-cone angle of the beam. The BSCs are evaluated using the numerical discrete spherical harmonics transform (DSHT). The far-field acoustic resonance scattering directivity diagrams are calculated for an albuminoidal shell immersed in water and filled with perfluoropropane gas, by subtracting an appropriate background from the total far-field form function. The properties related to the arbitrary scattering are analyzed and discussed. The results are of particular importance in acoustical scattering applications involving imaging and beam-forming for transducer design. Moreover, the GTRS method can be applied to investigate the scattering of any beam of arbitrary shape that satisfies the source-free Helmholtz equation, and the method can be readily adapted to viscoelastic spherical shells or spheres.

Bessel-function analysis of the optimized star coupler for uniform power splitting.

Science.gov (United States)

Song, G Hugh; Park, Mahn Yong

2004-08-01

An optimized N x N planar optic star coupler that utilizes directional coupling of arrayed waveguides for uniform power splitting is analyzed on the basis of special properties of the involved Bessel-function series. The analysis has provided a remarkably simple, novel basic design formula for such a device with much needed physical insights into the unique diffraction properties. For the analysis of diffraction from the end of directionally coupled arrayed waveguides, many useful formulas around the Bessel functions, such as the addition theorem and the Kepler-Bessel series, have been given in new forms.

A Limit Relation for Dunkl-Bessel Functions of Type A and B

Directory of Open Access Journals (Sweden)

Margit Rösler

2008-12-01

Full Text Available We prove a limit relation for the Dunkl-Bessel function of type BN with multiplicity parameters k_1 on the roots ±ei and k_2 on ±e_i±e_j where k_1 tends to infinity and the arguments are suitably scaled. It gives a good approximation in terms of the Dunkl-type Bessel function of type A_{N−1} with multiplicity k_2. For certain values of k_2 an improved estimate is obtained from a corresponding limit relation for Bessel functions on matrix cones.

Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging.

Science.gov (United States)

Thériault, Gabrielle; Cottet, Martin; Castonguay, Annie; McCarthy, Nathalie; De Koninck, Yves

2014-01-01

Two-photon microscopy has revolutionized functional cellular imaging in tissue, but although the highly confined depth of field (DOF) of standard set-ups yields great optical sectioning, it also limits imaging speed in volume samples and ease of use. For this reason, we recently presented a simple and retrofittable modification to the two-photon laser-scanning microscope which extends the DOF through the use of an axicon (conical lens). Here we demonstrate three significant benefits of this technique using biological samples commonly employed in the field of neuroscience. First, we use a sample of neurons grown in culture and move it along the z-axis, showing that a more stable focus is achieved without compromise on transverse resolution. Second, we monitor 3D population dynamics in an acute slice of live mouse cortex, demonstrating that faster volumetric scans can be conducted. Third, we acquire a stereoscopic image of neurons and their dendrites in a fixed sample of mouse cortex, using only two scans instead of the complete stack and calculations required by standard systems. Taken together, these advantages, combined with the ease of integration into pre-existing systems, make the extended depth-of-field imaging based on Bessel beams a strong asset for the field of microscopy and life sciences in general.

Generating Generalized Bessel Equations by Virtue of Bose Operator Algebra and Entangled State Representations

International Nuclear Information System (INIS)

Fan Hongyi; Wang Yong

2006-01-01

With the help of Bose operator identities and entangled state representation and based on our previous work [Phys. Lett. A 325 (2004) 188] we derive some new generalized Bessel equations which also have Bessel function as their solution. It means that for these intricate higher-order differential equations, we can get Bessel function solutions without using the expatiatory power-series expansion method.

F.W. Bessel (1825): The calculation of longitude and latitude from geodesic measurements

Science.gov (United States)

Karney, C. F. F.; Deakin, R. E.

2010-08-01

Issue No. 86 (1825 October) of the Astronomische Nachrichten was largely devoted to a single paper by F. W. Bessel on the solution of the direct geodesic problem (see the first sentences of the paper). For the most part, the paper stands on its own and needs little introduction. However, a few words are in order to place this paper in its historical context. First of all, it should be no surprise that a paper on this subject appeared in an astronomical journal. At the time, the disciplines of astronomy, navigation, and surveying were inextricably linked -- the methods and, in many cases, the practitioners (in particular, Bessel) were the same. Prior to Bessel's paper, the solution of the geodesic problem had been the subject of several studies by Clairaut, Euler, du Séjour, Legendre, Oriani, and others. The interest in the subject was twofold. It combined several new fields of mathematics: the calculus of variations, the theory of elliptic functions, and the differential geometry of curved surfaces. It also addressed very practical needs: the determination of the figure of the earth, the requirements of large scale surveys, and the construction of map projections. With the papers of Legendre and of Oriani in 1806, the framework for the mathematical solution for an ellipsoid of revolution had been established. However, Bessel was firmly in the practical camp; he carried out the East Prussian survey that connected the West European and Russian triangulation networks and later he made the first accurate estimate of the figure of the Earth, the ``Bessel ellipsoid''. He lays out his goal for this paper in its first section: to simplify the numerical solution of the geodesic problem. In Sects. \\ref{sec2}--\\ref{sec4}, Bessel gives a clear and concise summary of the previous work on the problem. In the remaining sections, he develops series for the distance and longitude integrals and constructs the tables which allow geodesics to be calculated to an accuracy of about 3

Bessel equation as an operator identity's matrix element in quantum mechanics

International Nuclear Information System (INIS)

Fan Hongyi; Li Chao

2004-01-01

We study the well-known Bessel equation itself in the framework of quantum mechanics. We show that the Bessel equation is a spontaneous result of an operator identity's matrix element in some definite entangled state representations, which is a fresh look. Application of this operator formalism in the Hankel transform of Laplace equation is presented

The Bessel-Struve intertwining operator on ℂ and mean-periodic functions

Directory of Open Access Journals (Sweden)

A. Gasmi

2004-01-01

Full Text Available We give a description of all transmutation operators from the Bessel-Struve operator to the second-derivative operator. Next we define and characterize the mean-periodic functions on the space ℋ of entire functions and we characterize the continuous linear mappings from ℋ into itself which commute with Bessel-Struve operator.

Evaluating the Financial Flows of Bessel Processes by Using Spectral Analysis

Directory of Open Access Journals (Sweden)

Burtnyak Ivan V.

2017-07-01

Full Text Available The article solves the two-parameter task of evaluating the intensity of diffuse Bessel processes by the methods of spectral theory. In particular, barriers for cost of options, where the derivative of financial flows turns into zero, have been considered, and a task for the two-barrier option has been solved, which corresponds to Bessel process. A Green’s function has been built for the diffusion Bessel process of the two-barrier option, decomposed according to the first-type system of Bessel functions. The barriers are taken in such a way that the derivative of financial flow in terms of price is turned to zero, i.e. there are the points where flow can acquire extreme values. On the basis of Green’s function, the value of securities has been calculated. It is handier to use similar barriers when monitoring a stock market. The Green’s function for this task, which represents the probability of spreading the option price, is represented through the Fourier series. This provides an opportunity to evaluate the intensity of financial flows in stock markets.

Research on Effective Electric-Mechanical Coupling Coefficient of Sandwich Type Piezoelectric Ultrasonic Transducer Using Bending Vibration Mode

Directory of Open Access Journals (Sweden)

Qiang Zhang

2015-01-01

Full Text Available An analytical model on electromechanical coupling coefficient and the length optimization of a bending piezoelectric ultrasonic transducer are proposed. The piezoelectric transducer consists of 8 PZT elements sandwiched between four thin electrodes, and the PZT elements are clamped by a screwed connection between fore beam and back beam. Firstly, bending vibration model of the piezoelectric transducer is built based on the Timoshenko beam theory. Secondly, the analytical model of effective electromechanical coupling coefficient is built based on the bending vibration model. Energy method and electromechanical equivalent circuit method are involved in the modelling process. To validate the analytical model, sandwich type piezoelectric transducer example in second order bending vibration mode is analysed. Effective electromechanical coupling coefficient of the transducer is optimized with simplex reflection technique, and the optimized ratio of length of the transducers is obtained. Finally, experimental prototypes of the sandwich type piezoelectric transducers are fabricated. Bending vibration mode and impedance of the experimental prototypes are tested, and electromechanical coupling coefficient is obtained according to the testing results. Results show that the analytical model is in good agreement with the experimental model.

Semi-analytical solution to arbitrarily shaped beam scattering

Science.gov (United States)

Wang, Wenjie; Zhang, Huayong; Sun, Yufa

2017-07-01

Based on the field expansions in terms of appropriate spherical vector wave functions and the method of moments scheme, an exact semi-analytical solution to the scattering of an arbitrarily shaped beam is given. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are presented to a spheroid and a circular cylinder of finite length, and the scattering properties are analyzed concisely.

A laboratory device for evaluation and study in the filed of ultrasonic transducers

International Nuclear Information System (INIS)

Vasiliu, S.

1978-12-01

A laboratory device for evaluation of the ultrasonic transducers, in view of adequate selection according to the testing requirements is presented. Recordings of ultrasonic beam of some transducers delivered as being of the same type are presented, showing important departures from specifications of the characteristics. Some of transducers evaluated have not been found acceptable for NDT in the nuclear field. (author)

Symbolic methods for the evaluation of sum rules of Bessel functions

International Nuclear Information System (INIS)

Babusci, D.; Dattoli, G.; Górska, K.; Penson, K. A.

2013-01-01

The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions. Furthermore, we obtain a set of new closed form sum rules involving various special polynomials and Bessel functions. The examples we consider are relevant for applications ranging from plasma physics to quantum optics

Characterization of the acoustic field generated by a horn shaped ultrasonic transducer

Science.gov (United States)

Hu, B.; Lerch, J. E.; Chavan, A. H.; Weber, J. K. R.; Tamalonis, A.; Suthar, K. J.; DiChiara, A. D.

2017-09-01

A horn shaped Langevin ultrasonic transducer used in a single axis levitator was characterized to better understand the role of the acoustic profile in establishing stable traps. The method of characterization included acoustic beam profiling performed by raster scanning an ultrasonic microphone as well as finite element analysis of the horn and its interface with the surrounding air volume. The results of the model are in good agreement with measurements and demonstrate the validity of the approach for both near and far field analyses. Our results show that this style of transducer produces a strong acoustic beam with a total divergence angle of 10°, a near-field point close to the transducer surface and a virtual sound source. These are desirable characteristics for a sound source used for acoustic trapping experiments.

Characterization of the acoustic field generated by a horn shaped ultrasonic transducer

Energy Technology Data Exchange (ETDEWEB)

Hu, B.; Lerch, J. E.; Chavan, A. H.; Weber, J. K. R.; Tamalonis, A.; Suthar, K. J.; DiChiara, A. D.

2017-09-04

A horn shaped Langevin ultrasonic transducer used in a single axis levitator was characterized to better understand the role of the acoustic profile in establishing stable traps. The method of characterization included acoustic beam profiling performed by raster scanning an ultrasonic microphone as well as finite element analysis of the horn and its interface with the surrounding air volume. The results of the model are in good agreement with measurements and demonstrate the validity of the approach for both near and far field analyses. Our results show that this style of transducer produces a strong acoustic beam with a total divergence angle of 10 degree, a near-field point close to the transducer surface and a virtual sound source. These are desirable characteristics for a sound source used for acoustic trapping experiments

Bessel functions in mass action modeling of memories and remembrances

Energy Technology Data Exchange (ETDEWEB)

Freeman, Walter J. [Department of Molecular and Cell Biology, University of California, Berkeley, CA 94720-3206 (United States); Capolupo, Antonio [Dipartimento di Fisica, E.R. Caianiello Universitá di Salerno, and INFN Gruppo collegato di Salerno, Fisciano 84084 (Italy); Kozma, Robert [Department of Mathematics, Memphis University, Memphis, TN 38152 (United States); Olivares del Campo, Andrés [The Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BZ (United Kingdom); Vitiello, Giuseppe, E-mail: vitiello@sa.infn.it [Dipartimento di Fisica, E.R. Caianiello Universitá di Salerno, and INFN Gruppo collegato di Salerno, Fisciano 84084 (Italy)

2015-10-02

Data from experimental observations of a class of neurological processes (Freeman K-sets) present functional distribution reproducing Bessel function behavior. We model such processes with couples of damped/amplified oscillators which provide time dependent representation of Bessel equation. The root loci of poles and zeros conform to solutions of K-sets. Some light is shed on the problem of filling the gap between the cellular level dynamics and the brain functional activity. Breakdown of time-reversal symmetry is related with the cortex thermodynamic features. This provides a possible mechanism to deduce lifetime of recorded memory. - Highlights: • We consider data from observations of impulse responses of cortex to electric shocks. • These data are fitted by Bessel functions which may be represented by couples of damped/amplified oscillators. • We study the data by using couples of damped/amplified oscillators. • We discuss lifetime and other properties of the considered brain processes.

Orthogonality, Lommel integrals and cross product zeros of linear combinations of Bessel functions.

Science.gov (United States)

Ziener, Christian H; Kurz, Felix T; Buschle, Lukas R; Kampf, Thomas

2015-01-01

The cylindrical Bessel differential equation and the spherical Bessel differential equation in the interval [Formula: see text] with Neumann boundary conditions are considered. The eigenfunctions are linear combinations of the Bessel function [Formula: see text] or linear combinations of the spherical Bessel functions [Formula: see text]. The orthogonality relations with analytical expressions for the normalization constant are given. Explicit expressions for the Lommel integrals in terms of Lommel functions are derived. The cross product zeros [Formula: see text] and [Formula: see text] are considered in the complex plane for real as well as complex values of the index [Formula: see text] and approximations for the exceptional zero [Formula: see text] are obtained. A numerical scheme based on the discretization of the two-dimensional and three-dimensional Laplace operator with Neumann boundary conditions is presented. Explicit representations of the radial part of the Laplace operator in form of a tridiagonal matrix allow the simple computation of the cross product zeros.

Comment on 'Analytical results for a Bessel function times Legendre polynomials class integrals'

International Nuclear Information System (INIS)

Cregg, P J; Svedlindh, P

2007-01-01

A result is obtained, stemming from Gegenbauer, where the products of certain Bessel functions and exponentials are expressed in terms of an infinite series of spherical Bessel functions and products of associated Legendre functions. Closed form solutions for integrals involving Bessel functions times associated Legendre functions times exponentials, recently elucidated by Neves et al (J. Phys. A: Math. Gen. 39 L293), are then shown to result directly from the orthogonality properties of the associated Legendre functions. This result offers greater flexibility in the treatment of classical Heisenberg chains and may do so in other problems such as occur in electromagnetic diffraction theory. (comment)

Random wandering of laser beams with orbital angular momentum during propagation through atmospheric turbulence.

Science.gov (United States)

Aksenov, Valerii P; Kolosov, Valeriy V; Pogutsa, Cheslav E

2014-06-10

The propagation of laser beams having orbital angular momenta (OAM) in the turbulent atmosphere is studied numerically. The variance of random wandering of these beams is investigated with the use of the Monte Carlo technique. It is found that, among various types of vortex laser beams, such as the Laguerre-Gaussian (LG) beam, modified Bessel-Gaussian beam, and hypergeometric Gaussian beam, having identical initial effective radii and OAM, the LG beam occupying the largest effective volume in space is the most stable one.

Vectorial analysis of the collimated beam of a small Gaussian source

Science.gov (United States)

Cao, Changqing; Wang, Ting; Zeng, Xiaodong; Feng, Zhejun; Zhang, Wenrui; Zhang, Xiaobing; Chen, Kun

2018-03-01

A vectorial analysis method to describe the collimated beam is proposed, the formulas of the intensity distribution and divergence angles represented in terms of Bessel functions are derived, and the propagation properties such as the vectorial structure of the collimated field and the shape of the beam spot are discussed in detail. Omitting the vectorial nature of the collimated beam can cause an error of 7.6% in determining the intensity distribution on the optical axis of the collimated beam.

Optimized Kaiser-Bessel Window Functions for Computed Tomography.

Science.gov (United States)

Nilchian, Masih; Ward, John Paul; Vonesch, Cedric; Unser, Michael

2015-11-01

Kaiser-Bessel window functions are frequently used to discretize tomographic problems because they have two desirable properties: 1) their short support leads to a low computational cost and 2) their rotational symmetry makes their imaging transform independent of the direction. In this paper, we aim at optimizing the parameters of these basis functions. We present a formalism based on the theory of approximation and point out the importance of the partition-of-unity condition. While we prove that, for compact-support functions, this condition is incompatible with isotropy, we show that minimizing the deviation from the partition of unity condition is highly beneficial. The numerical results confirm that the proposed tuning of the Kaiser-Bessel window functions yields the best performance.

Transverse particle dynamics in a Bessel beam

Czech Academy of Sciences Publication Activity Database

Milne, G.; Dholakia, K.; McGloin, D.; Volke-Sepulveda, K.; Zemánek, Pavel

2007-01-01

Roč. 15, č. 21 (2007), s. 13972-13987 ISSN 1094-4087 R&D Projects: GA MŠk(CZ) LC06007; GA MPO(CZ) FT-TA2/059 EU Projects: European Commission(XE) 508952 - ATOM3D Institutional research plan: CEZ:AV0Z20650511 Keywords : optical tweezers or optical manipulation * laser trapping * laser beam shaping Subject RIV: BH - Optics, Masers, Lasers Impact factor: 3.709, year: 2007

On sharp estimates of the convergence of double Fourier-Bessel series

Science.gov (United States)

Abilov, V. A.; Abilova, F. V.; Kerimov, M. K.

2017-11-01

The problem of approximation of a differentiable function of two variables by partial sums of a double Fourier-Bessel series is considered. Sharp estimates of the rate of convergence of the double Fourier-Bessel series on the class of differentiable functions of two variables characterized by a generalized modulus of continuity are obtained. The proofs of four theorems on this issue, which can be directly applied to solving particular problems of mathematical physics, approximation theory, etc., are presented.

A linear combination of modified Bessel functions

Science.gov (United States)

Shitzer, A.; Chato, J. C.

1971-01-01

A linear combination of modified Bessel functions is defined, discussed briefly, and tabulated. This combination was found to recur in the analysis of various heat transfer problems and in the analysis of the thermal behavior of living tissue when modeled by cylindrical shells.

Bessel-Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis.

Science.gov (United States)

Gutiérrez-Vega, Julio C; Rodríguez-Masegosa, Rodolfo; Chávez-Cerda, Sabino

2003-11-01

A detailed study of the axicon-based Bessel-Gauss resonator with concave output coupler is presented. We employ a technique to convert the Huygens-Fresnel integral self-consistency equation into a matrix equation and then find the eigenvalues and the eigenfields of the resonator at one time. A paraxial ray analysis is performed to find the self-consistency condition to have stable periodic ray trajectories after one or two round trips. The fast-Fourier-transform-based Fox and Li algorithm is applied to describe the three-dimensional intracavity field distribution. Special attention was directed to the dependence of the output transverse profiles, the losses, and the modal-frequency changes on the curvature of the output coupler and the cavity length. The propagation of the output beam is discussed.

Monotonicity and bounds on Bessel functions

Directory of Open Access Journals (Sweden)

Larry Landau

2000-07-01

Full Text Available survey my recent results on monotonicity with respect to order of general Bessel functions, which follow from a new identity and lead to best possible uniform bounds. Application may be made to the "spreading of the wave packet" for a free quantum particle on a lattice and to estimates for perturbative expansions.

Non-paraxial beam to push and pull microparticles

DEFF Research Database (Denmark)

Novitsky, Andrey; Qiu, C.-W.

2011-01-01

We discuss a feasibility of the pulling (backward) force acting on a spherical microparticle in a non-paraxial Bessel beam. The effect can be explained by the strong interaction of particle's multipoles or by the conservation of momentum in the system “photons-particle.” It is remarkable that the...

Propagation of obstructed Bessel and Bessel–Gauss beams

CSIR Research Space (South Africa)

Litvin, IA

2008-08-01

Full Text Available and phase of the beam after encountering an obstruction. Although this self reconstruction property has been previously modelled by numerous groups, the techniques involve rigorous, time-consuming computations. In this work we present an efficient method...

On the Computation and Applications of Bessel Functions with Pure Imaginary Indices

OpenAIRE

Matyshev, A. A.; Fohtung, E.

2009-01-01

Bessel functions with pure imaginary index (order) play an important role in corpuscular optics where they govern the dynamics of charged particles in isotrajectory quadrupoles. Recently they were found to be of great importance in semiconductor material characterization as they are manifested in the strain state of crystalline material. A new algorithm which can be used for the computation of the normal and modifed Bessel functions with pure imaginary index is proposed. The developed algorit...

Self-action of Bessel wave packets in a system of coupled light guides and formation of light bullets

Energy Technology Data Exchange (ETDEWEB)

Balakin, A. A., E-mail: balakin.alexey@yandex.ru; Mironov, V. A.; Skobelev, S. A., E-mail: sk.sa1981@gmail.com [Russian Academy of Sciences, Institute of Applied Physics (Russian Federation)

2017-01-15

The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrödinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the “kaleidoscopic” picture of a wave packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.

Generation of spirally polarized propagation-invariant beam using fiber microaxicon.

Science.gov (United States)

Philip, Geo M; Viswanathan, Nirmal K

2011-10-01

We present here a fiber microaxicon (MA)based method to generate spirally polarized propagation-invariant optical beam. MA chemically etched in the tip of a two-mode fiber efficiently converts the generic cylindrically polarized vortex fiber mode into a spirally polarized propagation-invariant (Bessel-type) beam via radial dependence of polarization rotation angle. The combined roles of helico-conical phase and nonparaxial propagation in the generation and characteristics of the output beam from the fiber MA are discussed. © 2011 Optical Society of America

Large degree asymptotics of generalized Bessel polynomials

NARCIS (Netherlands)

J.L. López; N.M. Temme (Nico)

2011-01-01

textabstractAsymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the

Instantaneous input electrical power measurements of HITU transducer

International Nuclear Information System (INIS)

Karaboece, B; Guelmez, Y; Rajagapol, S; Shaw, A

2011-01-01

HITU (High Intensity Theraupetic Ultrasound) transducers are widely used in therapeutic ultrasound in medicine. The output ultrasonic power of HITU transducer can be measured in number of methods described in IEC 61161 standard [1]. New IEC standards specifically for measurement of HITU equipment are under development. The ultrasound power radiated from a transducer is dependent on applied input electrical voltage and current and consequently power. But, up to now, no standardised method has been developed and adopted for the input electrical power measurements. Hence, a workpackage was carried out for the establishment of such method in the frequency range of 1 to 3 MHz as a part of EURAMET EMRP Era-net plus 'External Beam Cancer Therapy' project. Several current shunts were developed and evaluated. Current measurements were also realized with Philips current probe and preamplifier at NPL and Agilent current probe at UME. In this paper, a method for the measurement of instantaneous electrical power delivered to a reactive ultrasound transducer in the required frequency range is explored.

Instantaneous input electrical power measurements of HITU transducer

Energy Technology Data Exchange (ETDEWEB)

Karaboece, B; Guelmez, Y [Tuebitak Ulusal Metroloji Enstituesue (UME), P.K. 54 41470 Gebze-Kocaeli (Turkey); Rajagapol, S; Shaw, A, E-mail: baki.karaboce@ume.tubitak.gov.t [National Physical Laboratory (NPL), Hampton Road, Teddington TW11 0LW (United Kingdom)

2011-02-01

HITU (High Intensity Theraupetic Ultrasound) transducers are widely used in therapeutic ultrasound in medicine. The output ultrasonic power of HITU transducer can be measured in number of methods described in IEC 61161 standard [1]. New IEC standards specifically for measurement of HITU equipment are under development. The ultrasound power radiated from a transducer is dependent on applied input electrical voltage and current and consequently power. But, up to now, no standardised method has been developed and adopted for the input electrical power measurements. Hence, a workpackage was carried out for the establishment of such method in the frequency range of 1 to 3 MHz as a part of EURAMET EMRP Era-net plus 'External Beam Cancer Therapy' project. Several current shunts were developed and evaluated. Current measurements were also realized with Philips current probe and preamplifier at NPL and Agilent current probe at UME. In this paper, a method for the measurement of instantaneous electrical power delivered to a reactive ultrasound transducer in the required frequency range is explored.

Dynamic behaviour of non-uniform Bernoulli-Euler beams subjected ...

African Journals Online (AJOL)

This paper investigates the dynamics behaviour of non-uniform Bernoulli-Euler beams subjected to concentrated loads ravelling at variable velocities. The solution technique is based on the Generalized Galerkin Method and the use of the generating function of the Bessel function type. The results show that, for all the ...

Numerical model of the influence function of deformable mirrors based on Bessel Fourier orthogonal functions

International Nuclear Information System (INIS)

Li Shun; Zhang Sijiong

2014-01-01

A numerical model is presented to simulate the influence function of deformable mirror actuators. The numerical model is formed by Bessel Fourier orthogonal functions, which are constituted of Bessel orthogonal functions and a Fourier basis. A detailed comparison is presented between the new Bessel Fourier model, the Zernike model, the Gaussian influence function and the modified Gaussian influence function. Numerical experiments indicate that the new numerical model is easy to use and more accurate compared with other numerical models. The new numerical model can be used for describing deformable mirror performances and numerical simulations of adaptive optics systems. (research papers)

Development of transducers for integrated garter spring repositioning system

Energy Technology Data Exchange (ETDEWEB)

Sharma, B S.V.G.; Shyam, T V; Shrivastava, A K; Rupani, B B; Sinha, R K [Bhabha Atomic Research Centre, Bombay (India). Reactor Engineering Div.

1994-12-31

In order to reposition the dislocated garter springs in active channels of 235 MW Pressurised Heavy Water Reactors (PHWRs), a tool named as Integrated Garter Spring Repositioning System (INGRES) has been developed. The tool consists of transducers to detect the concentricity between the Pressure Tube (P/T) and Calandria Tube (C/T) and also to detect garter springs in the channel besides different modules for correcting the eccentricity between P/T and C/T and garter spring repositioning. The transducers used in the system namely Concentricity Detection Probe (CDP) and Garter Spring Detection Probe (GSDP) are based on the eddy current techniques. The CDP makes use of four eddy current bobbin probes separated 90 degrees apart in cross sectional plane of channel assembly. The transducer gives output signal in proportional to the air gap between P/T and C/T in two axes (X and Y) which are designed for the purpose. The output of the unit is obtained on the Cathode Ray Oscilloscope (CRO) screen in the form of illuminated dot. The dot position on the CRO screen gives the information about mismatch in concentricity between P/T and C/T of the channel. The GSDP meant for detecting garter springs in PHWR channel uses two sets of primary and secondary coils connected in differential mode. The output signals from the transducers are processed through a signal processing unit devised for the purpose to obtain output from it as a horizontal beam on the CRO screen. The garter spring presence in the channel is indicated by a change in the voltage level of beam and also by audio-visual indication in the form of buzzer and LED illumination on the processing unit. This paper gives general design and development aspects of the CDP and GSDP transducers of the INGRES tool. (author). 3 figs.

Expansion of infinite series containing modified Bessel functions of the second kind

International Nuclear Information System (INIS)

Fucci, Guglielmo; Kirsten, Klaus

2015-01-01

The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the parameters in the argument of the modified Bessel function of the second kind is small compared to the others. We apply the results obtained for the asymptotic expansion to specific problems that arise in the ambit of quantum field theory. (paper)

Second-order moments of Schell-model beams with various correlation functions in atmospheric turbulence.

Science.gov (United States)

Zheng, Guo; Wang, Jue; Wang, Lin; Zhou, Muchun; Xin, Yu; Song, Minmin

2017-11-15

The general formulae for second-order moments of Schell-model beams with various correlation functions in atmospheric turbulence are derived and validated by the Bessel-Gaussian Schell-model beams and cosine-Gaussian-correlated Schell-model beams. Our finding shows that the second-order moments of partially coherent Schell-model beams are related to the second-order partial derivatives of source spectral degree of coherence at the origin. The formulae we provide are much more convenient to analyze and research propagation problems in turbulence.

Further properties of the zeros of Bessel functions

Directory of Open Access Journals (Sweden)

Carla Giordano

1987-11-01

Full Text Available New monotonicity and convexity properties for the zeros cνk  (k=1,2,... of the Bessel functions are proved. New inequalities for cνk are also given. These inequalities are useful for small values of ν.

Note: Decoupling design for high frequency piezoelectric ultrasonic transducers with their clamping connections

Energy Technology Data Exchange (ETDEWEB)

Wang, F. J., E-mail: wangfujun@tju.edu.cn; Liang, C. M.; Tian, Y. L.; Zhao, X. Y.; Zhang, D. W. [Tianjin Key Laboratory of Equipment Design and Manufacturing Technology, School of Mechanical Engineering, Tianjin University, Tianjin 300072 (China); Zhang, H. J. [Tianjin Key Laboratory of Modern Mechatronics Equipment Technology, School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin 300387 (China)

2015-12-15

This work presents the flexure-mechanism based decoupling design between high frequency piezoelectric ultrasonic transducers and their clamping connections to improve ultrasonic energy transmission efficiency. The ring, prismatic beam, and circular notched hinge based flanges were presented, and the crucial geometric dimensions of the transducers with the flexure decoupling flanges were determined. Finite element analysis (FEA) was carried out to investigate the dynamic characteristics of the transducers. Finally, experiments were conducted to examine and verify the effects of the proposed decoupling flanges. FEA and experimental results show that smaller frequency deviations and larger tip displacement amplitudes have been achieved by using the transducers with the flexure flanges compared with the transducer with a rigid ring-type flange, and thus the ultrasonic transmission efficiency can be improved through the flexure flanges.

Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions.

Science.gov (United States)

Lötstedt, Erik; Jentschura, Ulrich D

2009-02-01

In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.

Approximate solutions of the hyperchaotic Rössler system by using the Bessel collocation scheme

Directory of Open Access Journals (Sweden)

Şuayip Yüzbaşı

2015-02-01

Full Text Available The purpose of this study is to give a Bessel polynomial approximation for the solutions of the hyperchaotic Rössler system. For this purpose, the Bessel collocation method applied to different problems is developed for the mentioned system. This method is based on taking the truncated Bessel expansions of the functions in the hyperchaotic Rössler systems. The suggested secheme converts the problem into a system of nonlinear algebraic equations by means of the matrix operations and collocation points, The accuracy and efficiency of the proposed approach are demonstrated by numerical applications and performed with the help of a computer code written in Maple. Also, comparison between our method and the differential transformation method is made with the accuracy of solutions.

On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind

Directory of Open Access Journals (Sweden)

Dinesh Kumar

2015-01-01

Full Text Available We develop a new and further generalized form of the fractional kinetic equation involving generalized Bessel function of the first kind. The manifold generality of the generalized Bessel function of the first kind is discussed in terms of the solution of the fractional kinetic equation in the paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably new results.

Construction of normal-regular decisions of Bessel typed special system

Science.gov (United States)

Tasmambetov, Zhaksylyk N.; Talipova, Meiramgul Zh.

2017-09-01

Studying a special system of differential equations in the separate production of the second order is solved by the degenerate hypergeometric function reducing to the Bessel functions of two variables. To construct a solution of this system near regular and irregular singularities, we use the method of Frobenius-Latysheva applying the concepts of rank and antirank. There is proved the basic theorem that establishes the existence of four linearly independent solutions of studying system type of Bessel. To prove the existence of normal-regular solutions we establish necessary conditions for the existence of such solutions. The existence and convergence of a normally regular solution are shown using the notion of rank and antirank.

Characterization of very high frequency transducers with wire target and hydrophone

International Nuclear Information System (INIS)

Huang Bin; Shung, K Kik

2004-01-01

In this paper, the wire-target technique will be shown to be a useful alternative for beam profile measurements in very high frequency range (30-60 MHz). A 9 cm long tungsten wire with a diameter of 8 μm was used as the pulse-echo target to measure the lateral beam profiles at the focal points of two transducers, a spherically focused 40 MHz Panametrics transducer with an aperture size of 6.35 mm and a geometrical focal length of 12.7 mm and a lense-focused in-house lithium niobate (LiNbO 3 ) 60 MHz transducer with an aperture size of 2 mm and a geometrical focal length around 6.5 mm. For comparison, measurements on the same transducers were performed by three small-aperture hydrophones. The first one is a polyvinylidene fluoride trifluoroethylene (PVDF-TrFE) membrane hydrophone developed by Hewlett-Packard, which has a geometric diameter of 37 μm, a measured effective diameter of less than 100 μm and a -3 dB bandwidth of more than 150 MHz. The second one is a needle-type PVDF hydrophone from Precision Acoustics, which has a 9 μm-thick PVDF element, a 40 μm geometrical aperture and a measured effective diameter of less than 100 μm. The third one is a needle-type PVDF hydrophone from Onda, which has a 150 μm geometrical aperture and an effective diameter of about 180 μm. Experimental results show that the -6 dB two-way beam widths measured by this 8 μm wire-target are in agreement with -3 dB transmitted beam widths measured by small-aperture hydrophones. Compared to small-aperture hydrophones, the wire-target technique is simpler and more cost-effective. Its major advantage however is in the frequency range above 100 MHz in which commercial hydrophones are not yet available

Ultrasonic flaw detection in a monorail box beam

Science.gov (United States)

Zheng, Peng; Greve, David W.; Oppenheim, Irving J.

2009-03-01

A steel box beam in a monorail application is constructed with an epoxy grout wearing surface, precluding visual inspection of its top flange. This paper describes a sequence of experimental research tasks to develop an ultrasonic system to detect flaws (such as fatigue cracks) in that flange, and the results of a field test to demonstrate system performance. The problem is constrained by the fact that the flange is exposed only along its longitudinal edges, and by the fact that permanent installation of transducers at close spacing was deemed to be impractical. The system chosen for development, after experimental comparison of alternate technologies, features angle-beam ultrasonic transducers with fluid coupling to the flange edge; the emitting transducers create transverse waves that travel diagonally across the width of the flange, where an array of receiving transducers detect flaw reflections and flaw shadows. The system rolls along the box beam, surveying (screening) the top flange for the presence of flaws. In a first research task, conducted on a full-size beam specimen, we compared waves generated from different transducer locations, either the flange edge or the web face, and at different frequency ranges. At relatively low frequencies, such as 100 kHz, we observed Lamb wave modes, and at higher frequency, in the MHz range, we observed nearlylongitudinal waves with trailing pulses. In all cases we observed little attenuation by the wearing surface and little influence of reflection at the web-flange joints. At the conclusion of this task we made the design decision to use edgemounted transducers at relatively high frequency, with correspondingly short wavelength, for best scattering from flaws. In a second research task we conducted experiments at 55% scale on a steel plate, with machined flaws of different size, and detected flaws of target size for the intended application. We then compared the performance of bonded transducers, fluid

Fractional Fourier transform for confluent hypergeometric beams

International Nuclear Information System (INIS)

Tang, Bin; Jiang, Chun; Zhu, Haibin

2012-01-01

Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system, the propagation properties of a new family of paraxial laser beams named confluent hypergeometric (HyG) beams, of which intensity profile is similar to that for the Bessel modes, passing through FRFT optical systems have been studied in detail by some typical numerical examples. The results indicate that the normalized intensity distribution of a HyG beam in the FRFT plane is closely related to not only the fractional order p but also the beam parameters m,n, and focal length f. -- Highlights: ► We study the propagation of a HyG beam through FRFT optical systems. ► The intensity of the beam in the FRFT plane is closely related to some parameters. ► We can control the properties of HyG beams by properly choosing the parameters.

Lead-free piezoelectric materials and ultrasonic transducers for medical imaging

Directory of Open Access Journals (Sweden)

Elaheh Taghaddos

2015-06-01

Full Text Available Piezoelectric materials have been vastly used in ultrasonic transducers for medical imaging. In this paper, firstly, the most promising lead-free compositions with perovskite structure for medical imaging applications have been reviewed. The electromechanical properties of various lead-free ceramics, composites, and single crystals based on barium titanate, bismuth sodium titanate, potassium sodium niobate, and lithium niobate are presented. Then, fundamental principles and design considerations of ultrasonic transducers are briefly described. Finally, recent developments in lead-free ultrasonic probes are discussed and their acoustic performance is compared to lead-based transducers. Focused transducers with different beam focusing methods such as lens focusing and mechanical shaping are explained. Additionally, acoustic characteristics of lead-free probes including the pulse-echo results as well as their imaging capabilities for various applications such as phantom imaging, in vitro intravascular ultrasound imaging of swine aorta, and in vivo or ex vivo imaging of human eyes and skin are reviewed.

A Novel Rotary Piezoelectric Motor Using First Bending Hybrid Transducers

Directory of Open Access Journals (Sweden)

Yingxiang Liu

2015-08-01

Full Text Available We report a novel rotary piezoelectric motor using bending transducers in this work. Three transducers are used to drive a disk-shaped rotor together by the elliptical movements of their driving tips; these motions are produced by the hybrid of two first bending vibration modes. The proposed piezoelectric transducer has a simple structure as it only contains an aluminum alloy beam and four pieces of PZT plates. Symmetrical structure is the only necessary condition in the design process as it will ensure the resonance frequencies of the two orthogonal first bending modes are equal. Transducers with first bending resonance frequency of about 53 kHz were fabricated and assembled into a rotary motor. The proposed motor exhibits good performance on speed and torque control. Under a working frequency of 53.2 kHz, the maximum no-load speed and the maximum torque of the prototype are tested to be 53.3 rpm and of 27 mN·m.

Studies on the Zeroes of Bessel Functions and Methods for Their Computation: IV. Inequalities, Estimates, Expansions, etc., for Zeros of Bessel Functions

Science.gov (United States)

Kerimov, M. K.

2018-01-01

This paper is the fourth in a series of survey articles concerning zeros of Bessel functions and methods for their computation. Various inequalities, estimates, expansions, etc. for positive zeros are analyzed, and some results are described in detail with proofs.

Generalized coherent states related to the associated Bessel functions and Morse potential

International Nuclear Information System (INIS)

Mojaveri, B; Amiri Faseghandis, S

2014-01-01

Using the associated Bessel functions, a shape-invariant Lie algebra spanned by ladder operators plus the identity operator, is realized. The Hilbert space of the associated Bessel functions, representing the Lie algebra, are established and two kinds of generalized coherent states as an appropriate superposition of these functions are constructed. By implying appropriate similarity transformation on the constructed coherent states, the generalized coherent states for the Morse potential are obtained. By considering some statistical characteristics, it is revealed that the constructed coherent states indeed possess nonclassical features, such as squeezing and sub-Poissonian statistics. (paper)

A new derivation of the plasma susceptibility tensor for a hot magnetized plasma without infinite sums of products of Bessel functions

International Nuclear Information System (INIS)

Qin Hong; Phillips, Cynthia K.; Davidson, Ronald C.

2007-01-01

The susceptibility tensor of a hot, magnetized plasma is conventionally expressed in terms of infinite sums of products of Bessel functions. For applications where the particle's gyroradius is larger than the wavelength, such as alpha particle dynamics interacting with lower-hybrid waves, and the focusing of charged particle beams using a solenoidal field, the infinite sums converge slowly. In this paper, a new derivation of the plasma susceptibility tensor is presented which exploits a symmetry in the particle's orbit to simplify the integration along the unperturbed trajectories. As a consequence, the infinite sums appearing in the conventional expression are replaced by definite double integrals over one gyroperiod, and the cyclotron resonances of all orders are captured by a single term. Furthermore, the double integrals can be carried out and expressed in terms of Bessel functions of complex order, in agreement with expressions deduced previously using the Newburger sum rule. From this new formulation, it is straightforward to derive the asymptotic form of the full hot plasma susceptibility tensor for a gyrotropic but otherwise arbitrary plasma distribution in the large gyroradius limit. These results are of more general importance in the numerical evaluation of the plasma susceptibility tensor. Instead of using the infinite sums occurring in the conventional expression, it is only necessary to evaluate the Bessel functions once according to the new expression, which has significant advantages, especially when the particle's gyroradius is large and the conventional infinite sums converge slowly. Depending on the size of the gyroradius, the computational saving enabled by this representation can be several orders-of-magnitude

Further 'comment on 'Generalized Bessel functions in tunnelling ionization''

International Nuclear Information System (INIS)

Reiss, H R; Krainov, V P

2005-01-01

J Bauer, in commenting on our tunnelling approximation for the generalized Bessel function, points out that when the approximation is applied to strong-field ionization, it is suitable only for the lowest-energy part of an ionization spectrum. We do not disagree. We point out several things: the results of Bauer are to be expected; linear polarization results are dominated by the lowest part of the multiphoton spectrum; and we do not recommend practical use of this tunnelling approximation, since the asymptotic approximation is so much better. We show comparisons of momentum distributions calculated with the tunnelling approximation and those with the complete strong-field approximation, which show in more detail than spectrum comparisons that the tunnelling approximation to the generalized Bessel function is applicable only to the low-momentum part of the distribution, and neglects altogether the high-momentum portion. (reply)

Inspection of complex geometry pieces with an intelligent contact transducer

International Nuclear Information System (INIS)

Chatillon, S.; Roy, O.; Mahaut, St.

2000-01-01

A new multi-element contact transducer has been developed to improve the inspection of components with complex geometry. The emitting surface is flexible in order to optimize the contact with pieces. An algorithm, based on a simplified geometric model, has been used to determine the delays law which allows to control the focal characteristics of the transmitted field. Acquisition data lead in transmission with an articulated transducer validate the behavior provided by simulation. Thus the optimization of the delays law ensures the transmission of a beam which is homogeneous and controlled during the moving of the transducer. Inspections in echo-pulse mode are implemented on a sample simulating a component controlled on site. Results show that the dynamical adaptation of the delays law to the geometry of the piece leads to very good performances

Quasi-fractional approximation to the Bessel functions

International Nuclear Information System (INIS)

Guerrero, P.M.L.

1989-01-01

In this paper the authors presents a simple Quasi-Fractional Approximation for Bessel Functions J ν (x), (- 1 ≤ ν < 0.5). This has been obtained by extending a method published which uses simultaneously power series and asymptotic expansions. Both functions, exact and approximated, coincide in at least two digits for positive x, and ν between - 1 and 0,4

Polarization holograms allow highly efficient generation of complex light beams.

Science.gov (United States)

Ruiz, U; Pagliusi, P; Provenzano, C; Volke-Sepúlveda, K; Cipparrone, Gabriella

2013-03-25

We report a viable method to generate complex beams, such as the non-diffracting Bessel and Weber beams, which relies on the encoding of amplitude information, in addition to phase and polarization, using polarization holography. The holograms are recorded in polarization sensitive films by the interference of a reference plane wave with a tailored complex beam, having orthogonal circular polarizations. The high efficiency, the intrinsic achromaticity and the simplicity of use of the polarization holograms make them competitive with respect to existing methods and attractive for several applications. Theoretical analysis, based on the Jones formalism, and experimental results are shown.

Calculating the Price for Derivative Financial Assets of Bessel Processes Using the Sturm-Liouville Theory

Directory of Open Access Journals (Sweden)

Burtnyak Ivan V.

2017-06-01

Full Text Available In the paper we apply the spectral theory to find the price for derivatives of financial assets assuming that the processes described are Markov processes and such that can be considered in the Hilbert space L^2 using the Sturm-Liouville theory. Bessel diffusion processes are used in studying Asian options. We consider the financial flows generated by the Bessel diffusions by expressing them in terms of the system of Bessel functions of the first kind, provided that they take into account the linear combination of the flow and its spatial derivative. Such expression enables calculating the size of the market portfolio and provides a measure of the amount of internal volatility in the market at any given moment, allows investigating the dynamics of the equity market. The expansion of the Green function in terms of the system of Bessel functions is expressed by an analytic formula that is convenient in calculating the volume of financial flows. All assumptions are natural, result in analytic formulas that are consistent with the empirical data and, when applied in practice, adequately reflect the processes in equity markets.

Studies on the zeros of Bessel functions and methods for their computation

Science.gov (United States)

Kerimov, M. K.

2014-09-01

The zeros of Bessel functions play an important role in computational mathematics, mathematical physics, and other areas of natural sciences. Studies addressing these zeros (their properties, computational methods) can be found in various sources. This paper offers a detailed overview of the results concerning the real zeros of the Bessel functions of the first and second kinds and general cylinder functions. The author intends to publish several overviews on this subject. In this first publication, works dealing with real zeros are analyzed. Primary emphasis is placed on classical results, which are still important. Some of the most recent publications are also discussed.

Asymmetric skew Bessel processes and their applications to finance

NARCIS (Netherlands)

Decamps, M.; Goovaerts, M.J.; Schoutens, W.

2006-01-01

In this paper, we extend the Harrison and Shepp's construction of the skew Brownian motion (1981) and we obtain a diffusion similar to the two-dimensional Bessel process with speed and scale densities discontinuous at one point. Natural generalizations to multi-dimensional and fractional order

The generalized Laguerre polynomials, the associated Bessel functions and application to propagation problems

International Nuclear Information System (INIS)

Dattoli, G.; Torre, A.; Mancho, A.M.

2000-01-01

The theory of generalized Bessel functions has found significant applications in the analysis of radiation phenomena, associated with charges moving in magnetic devices. In this paper we exploit the monomiality principle to discuss the theory of two-variable Laguerre polynomials and introduce the associated Laguerre-Bessel functions. We study their properties (addition and multiplication theorems, generating function, recurrence relations and so on) and discuss the link with the ordinary case. The usefulness of the obtained results to treat problems relevant to the paraxial propagation of electromagnetic waves is also discussed.

A spiral wave front beacon for underwater navigation: transducer prototypes and testing.

Science.gov (United States)

Dzikowicz, Benjamin R; Hefner, Brian T

2012-05-01

Transducers for acoustic beacons which can produce outgoing signals with wave fronts whose horizontal cross sections are circular or spiral are studied experimentally. A remote hydrophone is used to determine its aspect relative to the transducers by comparing the phase of the circular signal to the phase of the spiral signal. The transducers for a "physical-spiral" beacon are made by forming a strip of 1-3 piezocomposite transducer material around either a circular or spiral backing. A "phased-spiral" beacon is made from an array of transducer elements which can be driven either in phase or staggered out of phase so as to produce signals with either a circular or spiral wave front. Measurements are made to study outgoing signals and their usefulness in determining aspect angle. Vertical beam width is also examined and phase corrections applied when the hydrophone is out of the horizontal plane of the beacon. While numerical simulations indicate that the discontinuity in the physical-spiral beacon introduces errors into the measured phase, damping observed at the ends of the piezocomposite material is a more significant source of error. This damping is also reflected in laser Doppler vibrometer measurements of the transducer's surface velocity.

Transducer handbook user's directory of electrical transducers

CERN Document Server

Boyle, H B

2013-01-01

When selecting or using a particular type of transducer or sensor, there are a number of factors which must be considered. The question is not only for what kind of measurement, but under what physical conditions, constraints of accuracy, and to meet which service requirements, is a transducer needed? This handbook is designed to meet the selection needs of anyone specifying or using transducers with an electrical output. Each transducer is described in an easy-to-use tabular format, giving all of the necessary data including operating principles, applications, range limits, errors, over-range protection, supply voltage requirements, sensitivities, cross sensitivities, temperature ranges and sensitivities and signal conditioning needs. The author has added notes that reflect his broad practical experience. Added to this is an extensive worldwide suppliers directory.

Pressure transducers

International Nuclear Information System (INIS)

Gomes, A.V.

1975-01-01

Strain gauges pressure transducers types are presented. Models, characteristics and calibration procedures were also analysed. Initially, a theoretical study was accomplished to evaluate metallic alloys behavior on sensing elements manufacturing, and diaphragm was used as deflecting elements. Electrical models for potenciometric transducers were proposed at the beginning and subsequently comproved according our experiments. Concerning bridge transducers, existing models confirmed the conditions of linearity and sensitivity related to the electrical signal. All the work done was of help on the calibration field and pressure measurements employing unbounded strain gauge pressure transducers

The random phase transducer in ultrasonic NDT of coarse grain stainless steel

International Nuclear Information System (INIS)

Bordier, J.M.; Fink, M.; Le Brun, A.; Cohen-Tenoudji, F.

1993-11-01

Ultrasonic NDT of cast stainless steel is known to be difficult due to a huge loss of focussing of the ultrasonic beam, and to a high level speckle noise generated by the coarse grain structure. In this paper, we describe the principle of the ultrasonic random phase transducer. Experimental results are compared with those obtained with a standard spatial compound technique. We show that the random phase transducer is a good tool to characterize the multiple scattering process generated by these materials. (authors). 7 figs., 11 refs

Transducer-Mounting Fixture

Science.gov (United States)

Spiegel, Kirk W.

1990-01-01

Transducer-mounting fixture holds transducer securely against stud. Projects only slightly beyond stud after installation. Flanged transducer fits into fixture when hinged halves open. When halves reclosed, fixture tightened onto threaded stud until stud makes contact with transducer. Knurled area on fixture aids in tightening fixture on stud.

Multidimensional digital image representations using generalized Kaiser-Bessel window functions.

Science.gov (United States)

Lewitt, R M

1990-10-01

Inverse problems that require the solution of integral equations are inherent in a number of indirect imaging applications, such as computerized tomography. Numerical solutions based on discretization of the mathematical model of the imaging process, or on discretization of analytic formulas for iterative inversion of the integral equations, require a discrete representation of an underlying continuous image. This paper describes discrete image representations, in n-dimensional space, that are constructed by the superposition of shifted copies of a rotationally symmetric basis function. The basis function is constructed using a generalization of the Kaiser-Bessel window function of digital signal processing. The generalization of the window function involves going from one dimension to a rotationally symmetric function in n dimensions and going from the zero-order modified Bessel function of the standard window to a function involving the modified Bessel function of order m. Three methods are given for the construction, in n-dimensional space, of basis functions having a specified (finite) number of continuous derivatives, and formulas are derived for the Fourier transform, the x-ray transform, the gradient, and the Laplacian of these basis functions. Properties of the new image representations using these basis functions are discussed, primarily in the context of two-dimensional and three-dimensional image reconstruction from line-integral data by iterative inversion of the x-ray transform. Potential applications to three-dimensional image display are also mentioned.

Superiority of Bessel function over Zernicke polynomial as base ...

Indian Academy of Sciences (India)

Abstract. Here we describe the superiority of Bessel function as base function for radial expan- sion over Zernicke polynomial in the tomographic reconstruction technique. The causes for the superiority have been described in detail. The superiority has been shown both with simulated data for Kadomtsev's model for ...

Light-sheet generation in inhomogeneous media using self-reconstructing beams and the STED-principle.

Science.gov (United States)

Gohn-Kreuz, Cristian; Rohrbach, Alexander

2016-03-21

Self-reconstruction of Bessel beams in inhomogeneous media is beneficial in light-sheet based microscopy. Although the beam's ring system enables propagation stability, the resulting image contrast is reduced. Here, we show that by a combination of two self-reconstructing beams with different orbital angular momenta it is possible to inhibit fluorescence from the ring system by using stimulated emission depletion (STED) even in strongly scattering media. Our theoretical study shows that the remaining fluorescence γ depends non-linearly on the beams' relative radial and orbital angular momenta. For various scattering media we demonstrate that γ remains remarkably stable over long beam propagation distances.

Bulk Shear-Wave Transduction Experiments Using Magnetostrictive Transducers with a Thin Fe-Co Alloy Patch

Energy Technology Data Exchange (ETDEWEB)

Park, Jae Ha; Cho, Seung Hyun; Ahn, Bong Young; Kwon, Hyu Sang [Korea Research Institute of Standards and Science, Daejeon (Korea, Republic of)

2010-08-15

Recently, the results of many studies have clarified the successful performance of magnetostrictive transducers in which a ferromagnetic patch is used for the transduction of guided shear waves; this is because a thin ferromagnetic patch with strong magnetostriction is very useful for generating and detecting shear wave. This investigation deals with bulk shear wave transduction by means of magnetostriction; on the other hand, the existing studies have been focused on guided shear waves. A modular transducer was developed: this transducer comprised a coil, magnets, and a thin ferromagnetic patch that was made of Fe-Co alloy. Some experiments were conducted to verify the performance of the developed transducer. Radiation directivity pattern of the developed transducer was obtained, and a test to detect the damage on a side drill hole of a steel block specimen was carried out. From the results of these tests, the good performance of the transducer for nondestructive testing was verified on the basis of the signal-to-noise ratio and narrow beam directivity.

Analysis of optical vortices with suppressed sidelobes using modified Bessel-like function and trapezoid annulus modulation structures.

Science.gov (United States)

Guo, Jian; Wei, Zhongchao; Liu, Yuebo; Huang, Aili

2015-02-01

Two amplitude modulation methods, including modified Bessel-like function modulation structure and trapezoid annulus structure, for suppressing sidelobes of optical vortices are studied. In the former approach, we propose that the order of the Bessel-like function can be an additional parameter to modulate diffraction patterns of optical vortices motivated by the idea of conventional annulus structures. Furthermore, new Bessel-like modulation functions are introduced to solve the problem of low diffraction efficiency of the original one. Trapezoid annulus structure is proposed as a compromise structure between the modified Bessel-like modulation structure and the conventional annulus one, and has advantages of both. It is demonstrated that these two approaches can achieve high-quality optical vortices with suppressed sidelobes effectively, and the relative structures behave as more flexible and applicable structures for producing optical vortices with large coverage of topological charges, which suggests great potential in simplifying the structure designing procedure. These reliable and generalized structures for generating high-quality optical vortices will help to promote the development of future optical communication and optical manipulation significantly.

A simple derivation of new sum rules of Bessel functions

International Nuclear Information System (INIS)

Ciocci, F.; Dattoli, G.; Dipace, A.

1985-01-01

In this note it is exploited a recently suggested technique to get simple expressions for a class of sum rules of Bessel functions appearing in plasma physics; their relevance to the numerical evaluation of the Turkin function is also discussed

Annular phased array transducer for preclinical testing of anti-cancer drug efficacy on small animals.

Science.gov (United States)

Kujawska, Tamara; Secomski, Wojciech; Byra, Michał; Postema, Michiel; Nowicki, Andrzej

2017-04-01

A technique using pulsed High Intensity Focused Ultrasound (HIFU) to destroy deep-seated solid tumors is a promising noninvasive therapeutic approach. A main purpose of this study was to design and test a HIFU transducer suitable for preclinical studies of efficacy of tested, anti-cancer drugs, activated by HIFU beams, in the treatment of a variety of solid tumors implanted to various organs of small animals at the depth of the order of 1-2cm under the skin. To allow focusing of the beam, generated by such transducer, within treated tissue at different depths, a spherical, 2-MHz, 29-mm diameter annular phased array transducer was designed and built. To prove its potential for preclinical studies on small animals, multiple thermal lesions were induced in a pork loin ex vivo by heating beams of the same: 6W, or 12W, or 18W acoustic power and 25mm, 30mm, and 35mm focal lengths. Time delay for each annulus was controlled electronically to provide beam focusing within tissue at the depths of 10mm, 15mm, and 20mm. The exposure time required to induce local necrosis was determined at different depths using thermocouples. Location and extent of thermal lesions determined from numerical simulations were compared with those measured using ultrasound and magnetic resonance imaging techniques and verified by a digital caliper after cutting the tested tissue samples. Quantitative analysis of the results showed that the location and extent of necrotic lesions on the magnetic resonance images are consistent with those predicted numerically and measured by caliper. The edges of lesions were clearly outlined although on ultrasound images they were fuzzy. This allows to conclude that the use of the transducer designed offers an effective noninvasive tool not only to induce local necrotic lesions within treated tissue without damaging the surrounding tissue structures but also to test various chemotherapeutics activated by the HIFU beams in preclinical studies on small animals

Heat kernel analysis for Bessel operators on symmetric cones

DEFF Research Database (Denmark)

Möllers, Jan

2014-01-01

. The heat kernel is explicitly given in terms of a multivariable $I$-Bessel function on $Ω$. Its corresponding heat kernel transform defines a continuous linear operator between $L^p$-spaces. The unitary image of the $L^2$-space under the heat kernel transform is characterized as a weighted Bergmann space...

A theoretical study of cylindrical ultrasound transducers for intracavitary hyperthermia

International Nuclear Information System (INIS)

Lin, W.-L.; Fan, W.-C.; Yen, J.-Y.; Chen, Y.-Y.; Shieh, M.-J.

2000-01-01

Purpose: The purpose of this paper was to examine the heating patterns and penetration depth when a cylindrical ultrasound transducer is employed for intracavitary hyperthermia treatments. Methods and Materials: The present study employs a simulation program based on a simplified power deposition model for infinitely long cylindrical ultrasound transducers. The ultrasound power in the tissue is assumed to be exponentially attenuated according to the penetration depth of the ultrasound beam, and a uniform attenuation for the entire treatment region is also assumed. The distribution of specific absorption rate (SAR) ratio (the ratio of SAR for a point within the tissue to that for a specific point on the cavity surface) is used to determine the heating pattern for a set of given parameters. The parameters considered are the ultrasound attenuation in the tissue, the cavity size, and the transducer eccentricity. Results: Simulation results show that the ultrasound attenuation in the tissue, the cavity size, and the transducer eccentricity are the most influential parameters for the distribution of SAR ratio. A low frequency transducer located in a large cavity can produce a much better penetration. The cavity size is the major parameter affecting the penetration depth for a small cavity size, such as interstitial hyperthermia. The heating pattern can also be dramatically changed by the transducer eccentricity and radiating sector. In addition, for a finite length of cylindrical transducer, lower SAR ratio appears in the regions near the applicator's edges. Conclusion: The distribution of SAR ratio indicates the relationship between the treatable region and the parameters if an appropriate threshold of SAR ratio is taken. The findings of the present study comprehend whether or not a tumor is treatable, as well as select the optimal driving frequency, the appropriate cavity size, and the eccentricity of a cylindrical transducer for a specific treatment

CMB in a box: Causal structure and the Fourier-Bessel expansion

International Nuclear Information System (INIS)

Abramo, L. Raul; Reimberg, Paulo H.; Xavier, Henrique S.

2010-01-01

This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility γ=e -μ , where μ is the optical depth to Thomson scattering. We show that the contributions of order γ N to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z>>10 3 , effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position x-vector=0 and time t 0 . Hence, for each multipole l there is a discrete tower of momenta k il (not a continuum) which can affect physical observables, with the smallest momenta being k 1l ∼l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation - no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.

A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Nash, Patrick L.

2008-01-01

Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation Δ perpendicular FDA of 1/r (∂)/(∂r) r(∂)/(∂r) that possesses an associated exact unitary representation of e i/2λΔ perpendicular FDA . The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown to be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium

Acoustic non-diffracting Airy beam

International Nuclear Information System (INIS)

Lin, Zhou; Guo, Xiasheng; Tu, Juan; Ma, Qingyu; Wu, Junru; Zhang, Dong

2015-01-01

The acoustic non-diffracting Airy beam as its optical counterpart has unique features of self-bending and self-healing. The complexity of most current designs handicaps its applications. A simple design of an acoustic source capable of generating multi-frequency and broad-band acoustic Airy beam has been theoretically demonstrated by numerical simulations. In the design, a piston transducer is corrugated to induce spatial phase variation for transducing the Airy function. The piston's surface is grooved in a pattern that the width of each groove corresponds to the half wavelength of Airy function. The resulted frequency characteristics and its dependence on the size of the piston source are also discussed. This simple design may promote the wide applications of acoustic Airy beam particularly in the field of medical ultrasound

Compact and continuous embeddings of logarithmic Bessel potential spaces

Czech Academy of Sciences Publication Activity Database

Edmunds, D. E.; Gurka, P.; Opic, Bohumír

2005-01-01

Roč. 168, č. 3 (2005), s. 229-250 ISSN 0039-3223 R&D Projects: GA ČR(CZ) GA201/01/0333 Institutional research plan: CEZ:AV0Z10190503 Keywords : Bessel potential spaces * spaces of Hölder-continuous functions * Lorentz-Zygmund spaces Subject RIV: BA - General Mathematics Impact factor: 0.538, year: 2005

Auto-positioning ultrasonic transducer system

Science.gov (United States)

Buchanan, Randy K. (Inventor)

2010-01-01

An ultrasonic transducer apparatus and process for determining the optimal transducer position for flow measurement along a conduit outer surface. The apparatus includes a transmitting transducer for transmitting an ultrasonic signal, said transducer affixed to a conduit outer surface; a guide rail attached to a receiving transducer for guiding movement of a receiving transducer along the conduit outer surface, wherein the receiving transducer receives an ultrasonic signal from the transmitting transducer and sends a signal to a data acquisition system; and a motor for moving the receiving transducer along the guide rail, wherein the motor is controlled by a controller. The method includes affixing a transmitting transducer to an outer surface of a conduit; moving a receiving transducer on the conduit outer surface, wherein the receiving transducer is moved along a guide rail by a motor; transmitting an ultrasonic signal from the transmitting transducer that is received by the receiving transducer; communicating the signal received by the receiving transducer to a data acquisition and control system; and repeating the moving, transmitting, and communicating along a length of the conduit.

Development of ultrasonic testing equipment incorporating electromagnetic acoustic transducer

International Nuclear Information System (INIS)

Sato, Michio; Kimura, Motohiko; Okano, Hideharu; Miyazawa, Tatsuo; Nagase, Koichi; Ishikawa, Masaaki

1989-01-01

An ultrasonic testing equipment for use in in-service inspection of nuclear power plant piping has been developed, which comprises an angle-beam electromagnetic acoustic transducer mounted on a vehicle for scanning the piping surface to be inspected. The transducer functions without direct contact with the piping surface through couplant, and the vehicle does not require a guide track installed on the piping surface, being equipped with magnetic wheels that adhere to the piping material, permitting it to travel along the circumferential weld joint of a carbon steel pipe. The equipment thus dispenses with the laborious manual work involved in preparing the piping for inspection, such as removal of protective coating, surface polishing and installation of guide track and thereby considerably reduces the duration of inspection. The functioning principle and structural features of the transducer and vehicle are described, together with the results of trial operation of a prototype unit, which proved a 1mm deep notch cut on a test piece of 25mm thick carbon steel plate to be locatable with an accuracy of ±2mm. (author)

The nonlocal problem for a hyperbolic equation with Bessel operator in a rectangular domain

Directory of Open Access Journals (Sweden)

Natalya V. Zaitseva

2016-12-01

Full Text Available We consider a boundary value problem for a hyperbolic equation with Bessel differential operator in a rectangular domain with integral nonlocal boundary value condition of the first kind. The equivalence between boundary value problem with integral nonlocal condition of the first kind and a local boundary value problem with mixed boundary conditions of the first and third kinds is proved. The existence and uniqueness of solution of the equivalent problem are established by means of the spectral method. At the uniqueness proof the completeness of the eigenfunction system of the spectral problem is used . At the existence proof the assessment of coefficients of series, the asymptotic formula for Bessel function of the first kind and asymptotic formula for eigenvalues are used. Sufficient conditions on the functions defining initial data of the problem are received. The solution of the problem is obtained in explicit form. The solution is obtained in the form of the Fourier–Bessel series. Its convergence is proved in the class of regular solutions.

Vibration energy harvesting in a small channel fluid flow using piezoelectric transducer

Energy Technology Data Exchange (ETDEWEB)

Hassan, Md. Mehedi, E-mail: buetmehedi10@gmail.com; Hossain, Md. Yeam, E-mail: yeamhossain@gmail.com; Mazumder, Rakib, E-mail: rakibmazumder46075@gmail.com; Rahman, Roussel, E-mail: roussel.rahman@gmail.com; Rahman, Md. Ashiqur, E-mail: ashiqurrahman@me.buet.ac.bd [Department of Mechanical Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka-1000 (Bangladesh)

2016-07-12

This work is aimed at developing a way to harvest energy from a fluid stream with the application of piezoelectric transducers in a small channel. In this COMSOL Multiphysics based simulation study, it is attempted to harvest energy from the abundant renewable source of energy available in the form of kinetic energy of naturally occurring flow of fluids. The strategy involves harnessing energy from a fluid-actuator through generation of couples, eddies and vortices, resulting from the stagnation and separation of flow around a semi-circular bluff-body attached to a cantilever beam containing a piezoceramic layer. Fluctuation of fluidic pressure impulse on the beam due to vortex shedding and varying lift forces causes the flexible cantilever beam to oscillate in the direction normal to the fluid flow in a periodic manner. The periodic application and release of a mechanical strain upon the beam effected a generation of electric potential within the piezoelectric layer, thus enabling extraction of electrical energy from the kinetic energy of the fluid. The piezoelectric material properties and transducer design are kept unchanged throughout the study, whereas the configuration is tested with different fluids and varying flow characteristics. The size and geometry of the obstructing entity are systematically varied to closely inspect the output from different iterations and for finding the optimum design parameters. The intermittent changes in the generated forces and subsequent variation in the strain on the beam are also monitored to find definitive relationship with the electrical energy output.

A symmetric integral identity for Bessel functions with applications to integral geometry

Science.gov (United States)

Salman, Yehonatan

2017-12-01

In the article of Kunyansky (Inverse Probl 23(1):373-383, 2007) a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the unit sphere in Rn . The aim of this paper is to prove an analogous symmetric integral identity in case where our data for the spherical mean transform is given on an ellipse E in R2 . For this, we will use the recent results obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the expansions into eigenfunctions of Bessel functions of the first and second kind in elliptical coordinates.

High-dimensional structured light coding/decoding for free-space optical communications free of obstructions.

Science.gov (United States)

Du, Jing; Wang, Jian

2015-11-01

Bessel beams carrying orbital angular momentum (OAM) with helical phase fronts exp(ilφ)(l=0;±1;±2;…), where φ is the azimuthal angle and l corresponds to the topological number, are orthogonal with each other. This feature of Bessel beams provides a new dimension to code/decode data information on the OAM state of light, and the theoretical infinity of topological number enables possible high-dimensional structured light coding/decoding for free-space optical communications. Moreover, Bessel beams are nondiffracting beams having the ability to recover by themselves in the face of obstructions, which is important for free-space optical communications relying on line-of-sight operation. By utilizing the OAM and nondiffracting characteristics of Bessel beams, we experimentally demonstrate 12 m distance obstruction-free optical m-ary coding/decoding using visible Bessel beams in a free-space optical communication system. We also study the bit error rate (BER) performance of hexadecimal and 32-ary coding/decoding based on Bessel beams with different topological numbers. After receiving 500 symbols at the receiver side, a zero BER of hexadecimal coding/decoding is observed when the obstruction is placed along the propagation path of light.

Theory of generalized Bessel functions: Pt. 2

International Nuclear Information System (INIS)

Dattoli, G.; Torre, A.; Chiccoli, C.

1991-01-01

In this paper the systematic study of the generalized Bessel functions (GBF), recently introduced and often encountered in problems of scattering for which the dipole approximation is inadequate, is continuated. The relations among different GBF are analysed and their importance for the solution of differential finite-difference equation of the Raman-Nath type is discussed. Numerical results for the first-kind cylinder GBF in the preasymptotic region and also a preliminary analysis of the asymptotic properties of the modified GBF are presented

Cymbal and BB underwater transducers and arrays

Energy Technology Data Exchange (ETDEWEB)

Newnham, R.E.; Zhang, J.; Alkoy, S.; Meyer, R.; Hughes, W.J.; Hladky-Hennion, A.C.; Cochran, J.; Markley, D. [Materials Research Laboratory, Penn State University, University Park, PA 16802 (United States)

2002-09-01

The cymbal is a miniaturized class V flextensional transducer that was developed for use as a shallow water sound projector and receiver. Single elements are characterized by high Q, low efficiency, and medium power output capability. Its low cost and thin profile allow the transducer to be assembled into large flexible arrays. Efforts were made to model both single elements and arrays using the ATILA code and the integral equation formulation (EQI).Millimeter size microprobe hydrophones (BBs) have been designed and fabricated from miniature piezoelectric hollow ceramic spheres for underwater applications such as mapping acoustic fields of projectors, and flow noise sensors for complex underwater structures. Green spheres are prepared from soft lead zirconate titanate powders using a coaxial nozzle slurry process. A compact hydrophone with a radially-poled sphere is investigated using inside and outside electrodes. Characterization of these hydrophones is done through measurement of hydrostatic piezoelectric charge coefficients, free field voltage sensitivities and directivity beam patterns. (orig.)

Driving electrostatic transducers

DEFF Research Database (Denmark)

Nielsen, Dennis; Knott, Arnold; Andersen, Michael A. E.

2013-01-01

Electrostatic transducers represent a very interesting alternative to the traditional inefficient electrodynamic transducers. In order to establish the full potential of these transducers, power amplifiers which fulfill the strict requirements imposed by such loads (high impedance, frequency...... depended, nonlinear and high bias voltage for linearization) must be developed. This paper analyzes power stages and bias configurations suitable for driving an electrostatic transducer. Measurement results of a 300 V prototype amplifier are shown. Measuring THD across a high impedance source is discussed...

Spectral and spatial characteristics of third-harmonic generation in conical light beams

International Nuclear Information System (INIS)

Peet, V.E.; Shchemeljov, S.V.

2003-01-01

Generation of resonance-enhanced third harmonic in Bessel and other conical beams is analyzed from a simple picture, where the fundamental light field is decomposed into elementary configurations of crossed plain-wave sub-beams. We show that the overall harmonic output can be derived as a superposition of all partial harmonic components driven by elementary configurations of the fundamental field. Good agreement with experimental observations has been obtained in simulation of spectral and spatial characteristics of the generated third harmonic. Some peculiarities of harmonic generation in conical light fields are discussed

Electromechanical modelling of tapered ionic polymer metal composites transducers

Directory of Open Access Journals (Sweden)

Rakesha Chandra Dash

2016-09-01

Full Text Available Ionic polymer metal composites (IPMCs are relatively new smart materials that exhibit a bidirectional electromechanical coupling. IPMCs have large number of important engineering applications such as micro robotics, biomedical devices, biomimetic robotics etc. This paper presents a comparison between tapered and uniform cantilevered Nafion based IPMCs transducer. Electromechanical modelling is done for the tapered beam. Thickness can be varied according to the requirement of force and deflection. Numerical results pertaining to the force and deflection characteristics of both type IPMCs transducer are obtained. It is shown that the desired amount of force and deflections for tapered IPMCs can be achieved for a given voltage. Different fixed end (t0 and free end (t1 thickness values have been taken to justify the results using MATLAB.

Occupation times and exact asymptotics of small deviations of Bessel processes for Lp-norms with p>0

International Nuclear Information System (INIS)

Fatalov, V R

2007-01-01

We prove theorems on exact asymptotics of the distributions of integral functionals of the occupation time of Bessel processes. Using these results, we obtain exact asymptotics of small deviations for Bessel processes in the L p -norm. We use Laplace's method for the occupation times of Markov processes with continuous time. Computations are carried out for p=2 and p=1. We also solve extremal problems for the action functional

On functions defined by sums of products of Bessel functions

International Nuclear Information System (INIS)

Martin, P A

2008-01-01

Various functions, defined as infinite series of products of Bessel functions of the first kind, are studied. Integral representations are obtained, and then used to deduce asymptotic approximations. Although several methods have been investigated (including power series expansions and integral transforms), methods based on Fourier series emerge as the most useful

On the product and ratio of Bessel random variables

Directory of Open Access Journals (Sweden)

Saralees Nadarajah

2005-01-01

Full Text Available The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Bessel function random variables. An application of the results is provided by tabulating the associated percentage points.

A new concept of smart flexible phased array transducer to inspect component of complex geometry

International Nuclear Information System (INIS)

Roy, O.; Mauhaut, S.; Casula, O.; Cattiaux, G.

2001-01-01

In most of industries as aeronautics, aerospace and nuclear, the main part of the non destructive testing is carried out directly in touch with the inspected component. Among others, the cooling piping of French pressurized water reactor comprises many welding components with complex geometry: elbows, butt welds, nozzles. In service inspections of such components performed with conventional ultrasonic contact transducers present limited performances. First, variations in sensitivity, due to unmatched contact on depressions or irregular surface are observed, resulting in poor detection performances. In addition, the beam orientation transmitted through complex interfaces cannot be totally controlled, because of the disorientations suffered by the transducer during its displacement. As a result, the possible defect cannot be correctly detected, positioned and characterized. To overcome these difficulties and to improve the performances of such inspections, the French Atomic Energy Commission has developed a new concept of transducer, allowing both to take into account the varying profile of the tested component and to efficiently compensate these effects. This transducer is a flexible phased array able to match the surface of the inspected specimen and to efficiently compensate the deformation of its own surface, in order to preserve the ultrasonic beam characteristics in spite of the profile variations encountered during the scanning. This ability is achieved thanks to a specific instrumentation, which measures the deformation of the transducer radiating surface, made of individual ultrasonic elements mechanically jointed to fit the actual surface of the component being inspected. Inspections in pulse-echo mode have been performed on a specimen with an irregular profile containing artificial embedded reflectors. The comparison with inspection carried out using conventional transducer shows the efficiency of the system to characterize defects under such complex

Evaluation of a novel therapeutic focused ultrasound transducer based on Fermat’s spiral

Science.gov (United States)

Ramaekers, P.; de Greef, M.; Berriet, R.; Moonen, C. T. W.; Ries, M.

2017-06-01

The purpose of this study was to evaluate a novel phased array transducer design rule for therapeutic focused ultrasound applications. This design rule uses the discretized Fermat’s spiral to determine the positioning of the transducer elements for a given number of elements and f-number. Using this principle, three variations of Fermat’s spiral were generated, aimed at (1) grating lobe minimization, (2) side lobe minimization, and (3) an optimized element packing efficiency. For each spiral, sparse layouts using identical circular elements and fully populated layouts based on additional Voronoi tessellation were evaluated numerically. Evaluation criteria included the element size distribution, beam steering capabilities, focal plane pressure distribution, prefocal pressure distribution, and practical considerations. Finally, one Voronoi-tessellated design with a focal length and aperture diameter of 16 cm and a natural frequency of 1.3 MHz was evaluated experimentally through hydrophone measurements. The numerical evaluation showed that while sparse arrays possess superior beam steering capabilities for a given number of elements, the focal point quality and prefocal pressure distribution is substantially more favorable when using the Voronoi-tessellated designs. Beam steering was shown to be feasible with the tessellated designs for lateral deflections up to 10 mm and axial deflections up to 20 mm. The experimental evaluation showed that such a transducer is capable of inducing 40.00 MPa rarefactional and 237.50 MPa compressional peak pressure levels at 800 W instantaneous acoustic output power under free-field conditions, making the system potentially relevant for thermal ablation therapy, histotripsy applications, and shockwave-enhanced heating.

Investigation of factors affecting the calibration of strain gage based transducers (''Goodzeit gages'') for SSC magnets

International Nuclear Information System (INIS)

Davidson, M.; Gilbertson, A.; Dougherty, M.

1991-03-01

These transducers are designed to measure stresses on SSC collared coils. They are individually calibrated with a bonded ten-stack of SSC inner coil cable by applying a known load and reading corresponding output from the gages. The transducer is supported by a notched ''backing plate'' that allows for bending of the gage beam during calibration or in use with an actual coil. Several factors affecting the calibration and use of the transducers are: the number of times a ''backing plate'' is used, the similarities or difficulties between bonded ten-stacks, and the differences between the ten-stacks and the coil they represent. The latter is probably the most important because a calibration curve is a model of how a transducer should react within a coil. If the model is wrong, the calibration curve is wrong. Information will be presented regarding differences in calibrations between Brookhaven National Labs (also calibrating these transducers) and Fermilab -- what caused these differences, the investigation into the differences between coils and ten-stacks and how they relate to transducer calibration, and some suggestions for future calibrations

Acoustic transducer

Science.gov (United States)

Drumheller, Douglas S.

2000-01-01

An active acoustic transducer tool for use down-hole applications. The tool includes a single cylindrical mandrel including a shoulder defining the boundary of a narrowed portion over which is placed a sandwich-style piezoelectric tranducer assembly. The piezoelectric transducer assembly is prestressed by being placed in a thermal interference fit between the shoulder of the mandrel and the base of an anvil which is likewise positioned over the narrower portion of the mandrel. In the preferred embodiment, assembly of the tool is accomplished using a hydraulic jack to stretch the mandrel prior to emplacement of the cylindrical sandwich-style piezoelectric transducer assembly and anvil. After those elements are positioned and secured, the stretched mandrel is allowed to return substantially to its original (pre-stretch) dimensions with the result that the piezoelectric transducer elements are compressed between the anvil and the shoulder of the mandrel.

Dynamic hysteretic sensing model of bending-mode Galfenol transducer

International Nuclear Information System (INIS)

Cao, Shuying; Zheng, Jiaju; Sang, Jie; Zhang, Pengfei; Wang, Bowen; Huang, Wenmei

2015-01-01

A dynamic hysteretic sensing model has been developed to predict the dynamic responses of the magnetic induction, the stress, and the output voltage for a bending-mode Galfenol unimorph transducer subjected simultaneously to acceleration and bias magnetic field. This model is obtained by coupling the hysteretic Armstrong model and the structural dynamic model of the Galfenol unimorph beam. The structural dynamic model of the beam is founded based on the Euler-Bernouli beam theory, the nonlinear constitutive equations, and the Faraday law of electromagnetic induction. Comparisons between the calculated and measured results show the model can describe dynamic nonlinear voltage characteristics of the device, and can predict hysteretic behaviors between the magnetic induction and the stress. Moreover, the model can effectively analyze the effects of the bias magnetic field, the acceleration amplitude, and frequency on the root mean square voltage of the device

Dynamic hysteretic sensing model of bending-mode Galfenol transducer

Energy Technology Data Exchange (ETDEWEB)

Cao, Shuying, E-mail: shuying-cao@hebut.edu.cn; Zheng, Jiaju; Sang, Jie; Zhang, Pengfei; Wang, Bowen; Huang, Wenmei [Province-Ministry Joint Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability, Hebei University of Technology, Tianjin 300130 (China)

2015-05-07

A dynamic hysteretic sensing model has been developed to predict the dynamic responses of the magnetic induction, the stress, and the output voltage for a bending-mode Galfenol unimorph transducer subjected simultaneously to acceleration and bias magnetic field. This model is obtained by coupling the hysteretic Armstrong model and the structural dynamic model of the Galfenol unimorph beam. The structural dynamic model of the beam is founded based on the Euler-Bernouli beam theory, the nonlinear constitutive equations, and the Faraday law of electromagnetic induction. Comparisons between the calculated and measured results show the model can describe dynamic nonlinear voltage characteristics of the device, and can predict hysteretic behaviors between the magnetic induction and the stress. Moreover, the model can effectively analyze the effects of the bias magnetic field, the acceleration amplitude, and frequency on the root mean square voltage of the device.

Calibration of acoustic emission transducers

International Nuclear Information System (INIS)

Leschek, W.C.

1976-01-01

A method is described for calibrating an acoustic emission transducer to be used in a pre-set frequency range. The absolute reception sensitivity of a reference transducer is determined at frequencies selected within the frequency range. The reference transducer and the acoustic emission transducer are put into acoustic communication with the surface of a limited acoustic medium representing an equivalent acoustic load appreciably identical to that of the medium in which the use of the acoustic emission transducer is intended. A blank random acoustic noise is emitted in the acoustic medium in order to establish a diffuse and reverberating sound field, after which the output responses of the reference transducer and of the acoustic emission transducer are obtained with respect to the diffuse and reverberating field, for selected frequencies. The output response of the acoustic emission transducer is compared with that of the reference transducer for the selected frequencies, so as to determine the reception sensitivity of the acoustic emission transducer [fr

On a new class of integrals involving Bessel functions of the first kind

Directory of Open Access Journals (Sweden)

P. Agarwal

2014-06-01

Full Text Available In recent years, several integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas containing the Bessel function $J_\

On the Operator ⨁Bk Related to Bessel Heat Equation

Directory of Open Access Journals (Sweden)

Wanchak Satsanit

2010-01-01

Full Text Available We study the equation (∂/∂tu(x,t=c2⊕Bku(x,t with the initial condition u(x,0=f(x for x∈Rn+. The operator ⊕Bk is the operator iterated k-times and is defined by ⊕Bk=((∑i=1pBxi4-(∑j=p+1p+qBxi4k, where p+q=n is the dimension of the Rn+, Bxi=∂2/∂xi2+(2vi/xi(∂/∂xi, 2vi=2αi+1, αi>-1/2, i=1,2,3,…,n, and k is a nonnegative integer, u(x,t is an unknown function for (x,t=(x1,x2,…,xn,t∈Rn+×(0,∞, f(x is a given generalized function, and c is a positive constant. We obtain the solution of such equation, which is related to the spectrum and the kernel, which is so called Bessel heat kernel. Moreover, such Bessel heat kernel has interesting properties and also related to the kernel of an extension of the heat equation.

Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method.

Science.gov (United States)

Cagniot, Emmanuel; Fromager, Michael; Ait-Ameur, Kamel

2009-11-01

A variant of the Gaussian beam expansion method consists in expanding the Bessel function J0 appearing in the Fresnel-Kirchhoff integral into a finite sum of complex Gaussian functions to derive an analytical expression for a Laguerre-Gaussian beam diffracted through a hard-edge aperture. However, the validity range of the approximation depends on the number of expansion coefficients that are obtained by optimization-computation directly. We propose another solution consisting in expanding J0 onto a set of collimated Laguerre-Gaussian functions whose waist depends on their number and then, depending on its argument, predicting the suitable number of expansion functions to calculate the integral recursively.

Algorithm 831: modified Bessel functions of imaginary order and positive argument

NARCIS (Netherlands)

A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)

2004-01-01

textabstract77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions Kia (x), Lia (x) and their derivatives for real a and positive x; these functions are independent solutions of the differential equation x2w'' + xw' + (a2

Poynting vector and orbital angular momentum density of superpositions of Bessel beams

CSIR Research Space (South Africa)

Litvin, IA

2011-08-01

Full Text Available ?bal, and M. L. Calvo, ?Microparticle movements in optical funnels and pods,? Opt. Express 19(6), 5232?5243 (2011). 36. S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, ?Residue orbital angular momentum in interferenced double vortex beams with unequal... ???? ?? ??? ? ??? ? ???? ? ??? ? + +??? ? ??? ? + ? ??? ? ??? ? +??? ? ??? ? + ? +?? ? ? ? ?? ? ? ? + = ? (13) where we assume both fields are modulated by the same Gaussian beam of width w0, resulting in a Gaussian Rayleigh range of zr, and for brevity we have collapsed the phase terms related to the piston and Gouy phase shifts into the function ?(z...

Stability of cylindrical plasma in the Bessel function model

International Nuclear Information System (INIS)

Yamagishi, T.; Gimblett, C.G.

1988-01-01

The stability of free boundary ideal and tearing modes in a cylindrical plasma is studied by examining the discontinuity (Δ') of the helical flux function given by the force free Bessel function model at the singular surface. The m = O and m = 1 free boundary tearing modes become strongly unstable when the singular surface is just inside the plasma boundary for a wide range of longitudinal wave numbers. (author)

Extensions of Bessel sequences to dual pairs of frames

DEFF Research Database (Denmark)

Christensen, Ole; Kim, Hong Oh; Kim, Rae Young

2013-01-01

Tight frames in Hilbert spaces have been studied intensively for the past years. In this paper we demonstrate that it often is an advantage to use pairs of dual frames rather than tight frames. We show that in any separable Hilbert space, any pairs of Bessel sequences can be extended to a pair of...... be extended to a pair of dual frames. © 2012 Elsevier Inc. All rights reserved....

Reciprocal expansion of modified Bessel function in simple fractions and obtaining general summation relationships containing its zeros

Science.gov (United States)

Sherstyukov, V. B.; Sumin, E. V.

2017-12-01

Modified Bessel functions of the first kind Iv (z) (Infeld functions) where v > -1 are considered. Due to the constraint on the parameter v, all zeros of the function Iv (z) except z = 0 are simple, located on the imaginary axis by symmetric pairs and form an infinite countable set. On the basis on previous research of the authors dealing with general Bessel functions of the first kind Jv (z), a question about reciprocal expansion 1/Iv (z) in series of simple fractions of a certain structure (Krein’s series) is studied. The general formulas to calculate of special infinite sums containing degrees of Infeld function zeros are an important consequence of obtained expansion in simple fractions of the value 1/Iv (z) with any v > -1. The possibility of concrete definition of established summation relationships at different values of parameters and their connection with analogous relationships for the Bessel functions of the first kind Jv (z) is discussed.

On a family of Bessel type functions: Estimations, series, overconvergence

Science.gov (United States)

Paneva-Konovska, Jordanka

2017-12-01

A family of the Bessel-Maitland functions are considered in this paper and some useful estimations are obtained for them. Series defined by means of these functions are considered and their behaviour on the boundaries of the convergence domains is discussed. Using the obtained estimations, necessary and sufficient conditions for the series overconvergence, as well as Hadamard type theorem are proposed.

Performance evaluation of a drag-disc turbine transducer and three-beam gamma densitometer under transient two-phase flow conditions

International Nuclear Information System (INIS)

Nalezny, C.L.; Chen, L.L.; Solbrig, C.W.

1979-01-01

One of the primary variables measured in the Loss-of-Fluid Test (LOFT) Program is mass flow rate. LOFT uses drag-disc turbine tranducers (DTT) and a three-beam gamma densitometer to measure parameters from which mass flow may be computed. The transducer combination was performance tested under transient conditions in the blowdown loop at the LOFT Test Support Facility (LTSF). The performance tests consisted of three partial blowdowns of different durations starting from the same initial conditions. The reference mean mass flow rate was determined by measuring the amount of water required to reestablish initial conditions after each partial blowdown. The average mass flow rates computed from the output of the drag disc, turbine, and gamma densitometer were compared to the reference mean mass flow rates over three blowdown intervals. The tests indicated that the equal phase velocity mass measurement model provided excellent results through the use of the turbine and densitometer, and drag disc and densitometer when the phase velocities were nearly equal

Coalgebraising subsequential transducers

NARCIS (Netherlands)

H.H. Hansen (Helle); J. Adamek; C.A. Kupke (Clemens)

2008-01-01

htmlabstractSubsequential transducers generalise both classic deterministic automata and Mealy/Moore type state machines by combining (input) language recognition with transduction. In this paper we show that normalisation and taking differentials of subsequential transducers and their underlying

Studies on the zeros of Bessel functions and methods for their computation: 2. Monotonicity, convexity, concavity, and other properties

Science.gov (United States)

Kerimov, M. K.

2016-07-01

This work continues the study of real zeros of first- and second-kind Bessel functions and Bessel general functions with real variables and orders begun in the first part of this paper (see M.K. Kerimov, Comput. Math. Math. Phys. 54 (9), 1337-1388 (2014)). Some new results concerning such zeros are described and analyzed. Special attention is given to the monotonicity, convexity, and concavity of zeros with respect to their ranks and other parameters.

Coalgebraising Subsequential Transducers

NARCIS (Netherlands)

Hansen, H.H.

2008-01-01

Subsequential transducers generalise both classic deterministic automata and Mealy/Moore type state machines by combining (input) language recognition with transduction. In this paper we show that normalisation and taking differentials of subsequential transducers and their underlying structures can

Numerical evaluation of integrals containing a spherical Bessel function by product integration

International Nuclear Information System (INIS)

Lehman, D.R.; Parke, W.C.; Maximon, L.C.

1981-01-01

A method is developed for numerical evaluation of integrals with k-integration range from 0 to infinity that contain a spherical Bessel function j/sub l/(kr) explicitly. The required quadrature weights are easily calculated and the rate of convergence is rapid: only a relatively small number of quadrature points is needed: for an accurate evaluation even when r is large. The quadrature rule is obtained by the method of product integration. With the abscissas chosen to be those of Clenshaw--Curtis and the Chebyshev polynomials as the interpolating polynomials, quadrature weights are obtained that depend on the spherical Bessel function. An inhomogenous recurrence relation is derived from which the weights can be calculated without accumulation of roundoff error. The procedure is summarized as an easily implementable algorithm. Questions of convergence are discussed and the rate of convergence demonstrated for several test integrals. Alternative procedures are given for generating the integration weights and an error analysis of the method is presented

Computation of bessel functions in light scattering studies.

Science.gov (United States)

Ross, W D

1972-09-01

Computations of light scattering require finding Bessel functions of a series of orders. These are found most easily by recurrence, but excessive rounding errors may accumulate. Satisfactory procedures for cylinder and sphere functions are described. If argument z is real, find Y(n)(z) by recurrence to high orders. From two high orders of Y(n)(z) estimate J(n)(z). Use backward recurrence to maximum J(n)(z). Correct by forward recurrence to maximum. If z is complex, estimate high orders of J(n)(z) without Y(n)(z) and use backward recurrence.

Chromatic aberrations correction for imaging spectrometer based on acousto-optic tunable filter with two transducers.

Science.gov (United States)

Zhao, Huijie; Wang, Ziye; Jia, Guorui; Zhang, Ying; Xu, Zefu

2017-10-02

The acousto-optic tunable filter (AOTF) with wide wavelength range and high spectral resolution has long crystal and two transducers. A longer crystal length leads to a bigger chromatic focal shift and the double-transducer arrangement induces angular mutation in diffracted beam, which increase difficulty in longitudinal and lateral chromatic aberration correction respectively. In this study, the two chromatic aberrations are analyzed quantitatively based on an AOTF optical model and a novel catadioptric dual-path configuration is proposed to correct both the chromatic aberrations. The test results exhibit effectiveness of the optical configuration for this type of AOTF-based imaging spectrometer.

Development of a Flexible Broadband Rayleigh Waves Comb Transducer with Nonequidistant Comb Interval for Defect Detection of Thick-Walled Pipelines.

Science.gov (United States)

Zhao, Huamin; He, Cunfu; Yan, Lyu; Zhang, Haijun

2018-03-02

It is necessary to develop a transducer that can quickly detect the inner and outer wall defects of thick-walled pipes, in order to ensure the safety of such pipes. In this paper, a flexible broadband Rayleigh-waves comb transducer based on PZT (lead zirconate titanate) for defect detection of thick-walled pipes is studied. The multiple resonant coupling theory is used to expand the transducer broadband and the FEA (Finite Element Analysis) method is used to optimize transducer array element parameters. Optimization results show that the best array element parameters of the transducer are when the transducer array element length is 30 mm, the thickness is 1.2 mm, the width of one end of is 1.5 mm, and the other end is 3 mm. Based on the optimization results, such a transducer was fabricated and its performance was tested. The test results were consistent with the finite-element simulation results, and the -3 dB bandwidth of the transducer reached 417 kHz. Transducer directivity test results show that the Θ -3dB beam width was equal to 10 °, to meet the defect detection requirements. Finally, defects of thick-walled pipes were detected using the transducer. The results showed that the transducer could detect the inner and outer wall defects of thick-walled pipes within the bandwidth.

Modeling of ultrasound transducers

DEFF Research Database (Denmark)

Bæk, David

This Ph.D. dissertation addresses ultrasound transducer modeling for medical ultrasound imaging and combines the modeling with the ultrasound simulation program Field II. The project firstly presents two new models for spatial impulse responses (SIR)s to a rectangular elevation focused transducer...... (REFT) and to a convex rectangular elevation focused transducer (CREFT). These models are solvable on an analog time scale and give exact smooth solutions to the Rayleigh integral. The REFT model exhibits a root mean square (RMS) error relative to Field II predictions of 0.41 % at 3400 MHz, and 1.......37 % at 100MHz. The CREFT model exhibits a RMS deviation of 0.01 % relative to the exact numerical solution on a CREFT transducer. A convex non-elevation focused, a REFT, and a linear flat transducer are shown to be covered with the CREFT model as well. Pressure pulses calculated with a one...

3D-printed adaptive acoustic lens as a disruptive technology for transcranial ultrasound therapy using single-element transducers

Science.gov (United States)

Maimbourg, Guillaume; Houdouin, Alexandre; Deffieux, Thomas; Tanter, Mickael; Aubry, Jean-François

2018-01-01

The development of multi-element arrays for better control of the shape of ultrasonic beams has opened the way for focusing through highly aberrating media, such as the human skull. As a result, the use of brain therapy with transcranial-focused ultrasound has rapidly grown. Although effective, such technology is expensive. We propose a disruptive, low-cost approach that consists of focusing a 1 MHz ultrasound beam through a human skull with a single-element transducer coupled with a tailored silicone acoustic lens cast in a 3D-printed mold and designed using computed tomography-based numerical acoustic simulation. We demonstrate on N  =  3 human skulls that adding lens-based aberration correction to a single-element transducer increases the deposited energy on the target 10 fold.

Optimality of embeddings of Bessel-potential-type spaces into Lorentz-Karamata spaces

Czech Academy of Sciences Publication Activity Database

Gogatishvili, Amiran; Opic, Bohumír; Neves, J. S.

2004-01-01

Roč. 134, č. 6 (2004), s. 1127-1147 ISSN 0308-2105 R&D Projects: GA ČR GA201/01/0333 Institutional research plan: CEZ:AV0Z1019905 Keywords : slowly varying functions * Lorentz-Karamata spaces * Bessel potentials Subject RIV: BA - General Mathematics Impact factor: 0.487, year: 2004

On the validity of the use of a localized approximation for helical beams. I. Formal aspects

Science.gov (United States)

Gouesbet, Gérard; André Ambrosio, Leonardo

2018-03-01

The description of an electromagnetic beam for use in light scattering theories may be carried out by using an expansion over vector spherical wave functions with expansion coefficients expressed in terms of Beam Shape Coefficients (BSCs). A celebrated method to evaluate these BSCs has been the use of localized approximations (with several existing variants). We recently established that the use of any existing localized approximation is of limited validity in the case of Bessel and Mathieu beams. In the present paper, we address a warning against the use of any existing localized approximation in the case of helical beams. More specifically, we demonstrate that a procedure used to validate any existing localized approximation fails in the case of helical beams. Numerical computations in a companion paper will confirm that existing localized approximations are of limited validity in the case of helical beams.

Physical Applications of a Simple Approximation of Bessel Functions of Integer Order

Science.gov (United States)

Barsan, V.; Cojocaru, S.

2007-01-01

Applications of a simple approximation of Bessel functions of integer order, in terms of trigonometric functions, are discussed for several examples from electromagnetism and optics. The method may be applied in the intermediate regime, bridging the "small values regime" and the "asymptotic" one, and covering, in this way, an area of great…

Smart transducer with radiomodem

Science.gov (United States)

Pugach, V. N.; Voronin, E. L.

2018-04-01

Systems for measuring different parameters enabling metering and wireless data transmission are an urgent problem in the industry. One of the most promising solutions is the developments of metering instruments enabling radio-link and GSM data transmission. The article describes a transducer operating with temperature sensors of different types as well as with the sensors of other physical values with the output signal represented as current or voltage with subsequent measurement data transmission from the transducer to the computer via radio-link. The article provides transducer measurement accuracy check. The work confirmed the claimed temperature measurement accuracy, noted a stable data transmission via radio link and convenience of work with the transducer and software.

Characterization of Dielectric Electroactive Polymer transducers

DEFF Research Database (Denmark)

Nielsen, Dennis; Møller, Martin B.; Sarban, Rahimullah

2014-01-01

This paper analysis the small-signal model of the Dielectric Electro Active Polymer (DEAP) transducer. The DEAP transducer have been proposed as an alternative to the electrodynamic transducer in sound reproduction systems. In order to understand how the DEAP transducer works, and provide...

Bessel smoothing filter for spectral-element mesh

Science.gov (United States)

Trinh, P. T.; Brossier, R.; Métivier, L.; Virieux, J.; Wellington, P.

2017-06-01

Smoothing filters are extremely important tools in seismic imaging and inversion, such as for traveltime tomography, migration and waveform inversion. For efficiency, and as they can be used a number of times during inversion, it is important that these filters can easily incorporate prior information on the geological structure of the investigated medium, through variable coherent lengths and orientation. In this study, we promote the use of the Bessel filter to achieve these purposes. Instead of considering the direct application of the filter, we demonstrate that we can rely on the equation associated with its inverse filter, which amounts to the solution of an elliptic partial differential equation. This enhances the efficiency of the filter application, and also its flexibility. We apply this strategy within a spectral-element-based elastic full waveform inversion framework. Taking advantage of this formulation, we apply the Bessel filter by solving the associated partial differential equation directly on the spectral-element mesh through the standard weak formulation. This avoids cumbersome projection operators between the spectral-element mesh and a regular Cartesian grid, or expensive explicit windowed convolution on the finite-element mesh, which is often used for applying smoothing operators. The associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation. Significant scaling behaviour is obtained when comparing this strategy with the explicit convolution method. The theoretical numerical complexity of this approach increases linearly with the coherent length, whereas a sublinear relationship is observed practically. Numerical illustrations are provided here for schematic examples, and for a more realistic elastic full waveform inversion gradient smoothing on the SEAM II benchmark model. These examples illustrate well the

Studies on the zeros of Bessel functions and methods for their computation: 3. Some new works on monotonicity, convexity, and other properties

Science.gov (United States)

Kerimov, M. K.

2016-12-01

This paper continues the study of real zeros of Bessel functions begun in the previous parts of this work (see M. K. Kerimov, Comput. Math. Math. Phys. 54 (9), 1337-1388 (2014); 56 (7), 1175-1208 (2016)). Some new results regarding the monotonicity, convexity, concavity, and other properties of zeros are described. Additionally, the zeros of q-Bessel functions are investigated.

Air-Coupled Low Frequency Ultrasonic Transducers and Arrays with PMN-32%PT Piezoelectric Crystals

Directory of Open Access Journals (Sweden)

Rymantas J. Kazys

2017-01-01

Full Text Available Air-coupled ultrasonic techniques are being increasingly used for material characterization, non-destructive evaluation of composite materials using guided waves as well as for distance measurements. Application of those techniques is mainly limited by the big losses of ultrasonic signals due to attenuation and mismatch of the acoustic impedances of ultrasonic transducers and air. One of the ways to solve this problem is by application of novel more efficient piezoelectric materials like lead magnesium niobate-lead titanate (PMN-PT type crystals. The objective of this research was the development and investigation of low frequency (<50 kHz wide band air-coupled ultrasonic transducers and arrays with an improved performance using PMN-32%PT crystals. Results of finite element modelling and experimental investigations of the developed transducers and arrays are presented. For improvement of the performance strip-like matching elements made of low acoustic impedance, materials such as polystyrene foams were applied. It allowed to achieve transduction losses for one single element transducer −11.4 dB, what is better than of commercially available air-coupled ultrasonic transducers. Theoretical and experimental investigations of the acoustic fields radiated by the eight element ultrasonic array demonstrated not only a good performance of the array in a pulse mode, but also very good possibilities to electronically focus and steer the ultrasonic beam in space.

Multi-relaxation-time lattice Boltzmann modeling of the acoustic field generated by focused transducer

Science.gov (United States)

Shan, Feng; Guo, Xiasheng; Tu, Juan; Cheng, Jianchun; Zhang, Dong

The high-intensity focused ultrasound (HIFU) has become an attractive therapeutic tool for the noninvasive tumor treatment. The ultrasonic transducer is the key component in HIFU treatment to generate the HIFU energy. The dimension of focal region generated by the transducer is closely relevant to the safety of HIFU treatment. Therefore, it is essential to numerically investigate the focal region of the transducer. Although the conventional acoustic wave equations have been used successfully to describe the acoustic field, there still exist some inherent drawbacks. In this work, we presented an axisymmetric isothermal multi-relaxation-time lattice Boltzmann method (MRT-LBM) model with the Bouzidi-Firdaouss-Lallemand (BFL) boundary condition in cylindrical coordinate system. With this model, some preliminary simulations were firstly conducted to determine a reasonable value of the relaxation parameter. Then, the validity of the model was examined by comparing the results obtained with the LBM results with the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and the Spheroidal beam equation (SBE) for the focused transducers with different aperture angles, respectively. In addition, the influences of the aperture angle on the focal region were investigated. The proposed model in this work will provide significant references for the parameter optimization of the focused transducer for applications in the HIFU treatment or other fields, and provide new insights into the conventional acoustic numerical simulations.

Wide-beam sensors for controlling dual-delay systems

Science.gov (United States)

Edwards, J. B.; Twemlow, J. K.

1982-09-01

A class of dual delay feedback systems of open loop transfer function G(s) = k exp(-Xs)/l - exp(-Ws) is shown to be unstable if ratio X/W is noninteger. By means of z-transform techniques it is shown that, by using a feedback transducer that senses over a substantial distance either side of its central axis, closed-loop stability may be restored. Such transducers, termed widebeam sensors, include transmission, backscatter and natural radiation types as well as electromechanical conveyor belt weighers. Designing transducers for very narrow beams may not be desirable from the overall system viewpoint.

Crossflow force transducer

International Nuclear Information System (INIS)

Mulcahy, T.M.

1982-05-01

A force transducer for measuring lift and drag coefficients for a circular cylinder in turbulent water flow is presented. In addition to describing the actual design and construction of the strain-gauged force- ring based transducer, requirements for obtained valid fluid force test data are discussed, and pertinent flow test experience is related

Handbook of force transducers

CERN Document Server

Stefanescu, Dan Mihai

2011-01-01

Part I introduces the basic ""Principles and Methods of Force Measurement"" acording to a classification into a dozen of force transducers types: resistive, inductive, capacitive, piezoelectric, electromagnetic, electrodynamic, magnetoelastic, galvanomagnetic (Hall-effect), vibrating wires, (micro)resonators, acoustic and gyroscopic. Two special chapters refer to force balance techniques and to combined methods in force measurement. Part II discusses the ""(Strain Gauge) Force Transducers Components"", evolving from the classical force transducer to the digital / intelligent one, with the inco

Micromachined capacitive ultrasonic immersion transducer array

Science.gov (United States)

Jin, Xuecheng

Capacitive micromachined ultrasonic transducers (cMUTs) have emerged as an attractive alternative to conventional piezoelectric ultrasonic transducers. They offer performance advantages of wide bandwidth and sensitivity that have heretofore been attainable. In addition, micromachining technology, which has benefited from the fast-growing microelectronics industry, enables cMUT array fabrication and electronics integration. This thesis describes the design and fabrication of micromachined capacitive ultrasonic immersion transducer arrays. The basic transducer electrical equivalent circuit is derived from Mason's theory. The effects of Lamb waves and Stoneley waves on cross coupling and acoustic losses are discussed. Electrical parasitics such as series resistance and shunt capacitance are also included in the model of the transducer. Transducer fabrication technology is systematically studied. Device dimension control in both vertical and horizontal directions, process alternatives and variations in membrane formation, via etch and cavity sealing, and metalization as well as their impact on transducer performance are summarized. Both 64 and 128 element 1-D array transducers are fabricated. Transducers are characterized in terms of electrical input impedance, bandwidth, sensitivity, dynamic range, impulse response and angular response, and their performance is compared with theoretical simulation. Various schemes for cross coupling reduction is analyzed, implemented, and verified with both experiments and theory. Preliminary results of immersion imaging are presented using 64 elements 1-D array transducers for active source imaging.

Circuit for Driving Piezoelectric Transducers

Science.gov (United States)

Randall, David P.; Chapsky, Jacob

2009-01-01

The figure schematically depicts an oscillator circuit for driving a piezoelectric transducer to excite vibrations in a mechanical structure. The circuit was designed and built to satisfy application-specific requirements to drive a selected one of 16 such transducers at a regulated amplitude and frequency chosen to optimize the amount of work performed by the transducer and to compensate for both (1) temporal variations of the resonance frequency and damping time of each transducer and (2) initially unknown differences among the resonance frequencies and damping times of different transducers. In other words, the circuit is designed to adjust itself to optimize the performance of whichever transducer is selected at any given time. The basic design concept may be adaptable to other applications that involve the use of piezoelectric transducers in ultrasonic cleaners and other apparatuses in which high-frequency mechanical drives are utilized. This circuit includes three resistor-capacitor networks that, together with the selected piezoelectric transducer, constitute a band-pass filter having a peak response at a frequency of about 2 kHz, which is approximately the resonance frequency of the piezoelectric transducers. Gain for generating oscillations is provided by a power hybrid operational amplifier (U1). A junction field-effect transistor (Q1) in combination with a resistor (R4) is used as a voltage-variable resistor to control the magnitude of the oscillation. The voltage-variable resistor is part of a feedback control loop: Part of the output of the oscillator is rectified and filtered for use as a slow negative feedback to the gate of Q1 to keep the output amplitude constant. The response of this control loop is much slower than 2 kHz and, therefore, does not introduce significant distortion of the oscillator output, which is a fairly clean sine wave. The positive AC feedback needed to sustain oscillations is derived from sampling the current through the

Focused ultrasound transducer spatial peak intensity estimation: a comparison of methods

Science.gov (United States)

Civale, John; Rivens, Ian; Shaw, Adam; ter Haar, Gail

2018-03-01

Characterisation of the spatial peak intensity at the focus of high intensity focused ultrasound transducers is difficult because of the risk of damage to hydrophone sensors at the high focal pressures generated. Hill et al (1994 Ultrasound Med. Biol. 20 259-69) provided a simple equation for estimating spatial-peak intensity for solid spherical bowl transducers using measured acoustic power and focal beamwidth. This paper demonstrates theoretically and experimentally that this expression is only strictly valid for spherical bowl transducers without a central (imaging) aperture. A hole in the centre of the transducer results in over-estimation of the peak intensity. Improved strategies for determining focal peak intensity from a measurement of total acoustic power are proposed. Four methods are compared: (i) a solid spherical bowl approximation (after Hill et al 1994 Ultrasound Med. Biol. 20 259-69), (ii) a numerical method derived from theory, (iii) a method using measured sidelobe to focal peak pressure ratio, and (iv) a method for measuring the focal power fraction (FPF) experimentally. Spatial-peak intensities were estimated for 8 transducers at three drive powers levels: low (approximately 1 W), moderate (~10 W) and high (20-70 W). The calculated intensities were compared with those derived from focal peak pressure measurements made using a calibrated hydrophone. The FPF measurement method was found to provide focal peak intensity estimates that agreed most closely (within 15%) with the hydrophone measurements, followed by the pressure ratio method (within 20%). The numerical method was found to consistently over-estimate focal peak intensity (+40% on average), however, for transducers with a central hole it was more accurate than using the solid bowl assumption (+70% over-estimation). In conclusion, the ability to make use of an automated beam plotting system, and a hydrophone with good spatial resolution, greatly facilitates characterisation of the FPF, and

Bessel function expansion to reduce the calculation time and memory usage for cylindrical computer-generated holograms.

Science.gov (United States)

Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko

2017-07-10

This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.

Asymptotic formulae for the Lommel and Bessel functions and their derivatives.

Science.gov (United States)

Aleksandrova, N I

2014-10-01

We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the same method, we obtain previously known approximate representations of the Nicholson type for Bessel functions and their first derivatives. We study also for what values of the parameters our representations have reasonable accuracy.

Dispersion relation for Bernstein waves using a new transformation for the modified Bessel function

International Nuclear Information System (INIS)

Sato, Masumi

1985-01-01

Aitken's or Shanks' transformation of the exponent-modified Bessel function produces better approximations. Dispersion relations for the hybrid and Bernstein waves using these provide better thermal and parallel wavenumber corrections. They also predict more closely the evolution and mode-conversion of these waves. (author)

Limited Diffraction Maps for Pulsed Wave Annular Arrays

DEFF Research Database (Denmark)

Fox, Paul D.

2002-01-01

A procedure is provided for decomposing the linear field of flat pulsed wave annular arrays into an equivalent set of known limited diffraction Bessel beams. Each Bessel beam propagates with known characteristics, enabling good insight into the propagation of annular fields to be obtained...

Azimuthal decomposition with digital holograms

CSIR Research Space (South Africa)

Litvin, IA

2012-05-01

Full Text Available , i.e., practically real- time acquisition of the necessary data. 4. Results and discussion 4.1. Superposition of two OAM carrying Bessel beams To test the accuracy of the method, we first created a superposition of two Bessel beams with opposite...

Micromachined Integrated Transducers for Ultrasound Imaging

DEFF Research Database (Denmark)

la Cour, Mette Funding

The purpose of this project is to develop capacitive micromachined ultrasonic transducers (CMUTs) for medical imaging. Medical ultrasound transducers used today are fabricated using piezoelectric materials and bulk processing. To fabricate transducers capable of delivering a higher imaging...

Programming macro tree transducers

DEFF Research Database (Denmark)

Bahr, Patrick; Day, Laurence E.

2013-01-01

transducers can be concisely represented in Haskell, and demonstrate the benefits of utilising such an approach with a number of examples. In particular, tree transducers afford a modular programming style as they can be easily composed and manipulated. Our Haskell representation generalises the original...

Analytic approximation for the modified Bessel function I -2/3(x)

Science.gov (United States)

Martin, Pablo; Olivares, Jorge; Maass, Fernando

2017-12-01

In the present work an analytic approximation to modified Bessel function of negative fractional order I -2/3(x) is presented. The validity of the approximation is for every positive value of the independent variable. The accuracy is high in spite of the small number (4) of parameters used. The approximation is a combination of elementary functions with rational ones. Power series and assymptotic expansions are simultaneously used to obtain the approximation.

A generalization for the infinite integral over three spherical Bessel functions

International Nuclear Information System (INIS)

Mehrem, R; Hohenegger, A

2010-01-01

A new formula is derived that generalizes an earlier result for the infinite integral over three spherical Bessel functions. The analytical result involves a finite sum over associated Legendre functions, P m l (x) of degree l and order m. The sum allows for the values of |m| that are greater than l. A generalization for the associated Legendre functions to allow for any rational m for a specific l is also shown.

A Direct Driver for Electrostatic Transducers

DEFF Research Database (Denmark)

Nielsen, Dennis; Knott, Arnold; Andersen, Michael A. E.

2014-01-01

Electrostatic transducers represent a very interesting alternative to the traditional inefficient electrodynamic transducers. In order to establish the full potential of these transducers, power amplifiers which fulfill the strict requirements imposed by such loads (high impedance, frequency...... depended, nonlinear and high bias voltage for linearization) must be developed. This paper analyzes a power stage suitable for driving an electrostatic transducer under biasing. Measurement results of a ±400 V prototype amplifier are shown. THD below 1% is reported....

Vibration transducer calibration techniques

Science.gov (United States)

Brinkley, D. J.

1980-09-01

Techniques for the calibration of vibration transducers used in the Aeronautical Quality Assurance Directorate of the British Ministry of Defence are presented. Following a review of the types of measurements necessary in the calibration of vibration transducers, the performance requirements of vibration transducers, which can be used to measure acceleration, velocity or vibration amplitude, are discussed, with particular attention given to the piezoelectric accelerometer. Techniques for the accurate measurement of sinusoidal vibration amplitude in reference-grade transducers are then considered, including the use of a position sensitive photocell and the use of a Michelson laser interferometer. Means of comparing the output of working-grade accelerometers with that of previously calibrated reference-grade devices are then outlined, with attention given to a method employing a capacitance bridge technique and a method to be used at temperatures between -50 and 200 C. Automatic calibration procedures developed to speed up the calibration process are outlined, and future possible extensions of system software are indicated.

Roots of two transcendental equations involving spherical bessel functions

International Nuclear Information System (INIS)

Pexton, R.L.; Steiger, A.D.

1977-01-01

Roots of the transcendental equations j/sub l/(αlambda) y/sub l/(lambda) =j/sub l/(lambda) y/sub l/(αlambda) and [xj/sub l/(x)]'/sub x alphaeta yl-italic/(x)]'/sub x eta/=xj/sub l/(x)]'/sub x eta yl-italic/(x)]'/sub x alphaeta/for the spherical Bessel functions of the first and second kind, j/sub l/(z) and y/sub l/(z), have been computed. The ranges for the parameter α, the order l and the root index n are: α=0.1(0.1)0.7,l=1(1)15,n=1(1)30

NMR signal transducer

International Nuclear Information System (INIS)

Kucheryaev, A.G.; Oliferchuk, N.L.

1975-01-01

A signal transducer of nuclear magnetic resonance for simultaneously measuring frequency and intensitivity of two various isotope signals, which are in one specimen is described. The transducer represents radiofrequency circuit with two resonance frequences, which is common for two autodyne generators. To decrease measuring time and to increase recording diagram stability the radiofrequency circuit has LC netork, in the inductivity of which investigated specimen is located; a circuit variable capacity is connected in parallel with one of the autodyne generators. Besides the radiofrequency circuit has an inductance coil in series with a standard specimen inside as well as a variable capacitor connected in parallel with the second autodyne generator. An amplitude of oscillation of each resonance frequency is controlled and adjusted separately. The transducer described can be used for the measurement of a nuclei concentration, isotope concentration and for the spin determination

Elliptic integral evaluations of Bessel moments and applications

International Nuclear Information System (INIS)

Bailey, David H; Borwein, Jonathan M; Broadhurst, David; Glasser, M L

2008-01-01

We record and substantially extend what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical physics. In particular, we develop formulae for integrals of products of six or fewer Bessel functions. In consequence, we are able to discover and prove closed forms for c n,k := ∫ ∞ 0 t k K n 0 (t) dt with integers n 1, 2, 3, 4 and k ≥ 0, obtaining new results for the even moments c 3,2k and c 4,2k . We also derive new closed forms for the odd moments s n,2k+1 := ∫ ∞ 0 t 2k+1 I 0 (t)K n-1 0 (t) dt with n = 3, 4 and for t n,2k+1 :∫ ∞ 0 t 2k+1 I 2 0 (t)K n-2 0 (t) dt with n = 5, relating the latter to Green functions on hexagonal, diamond and cubic lattices. We conjecture the values of s 5,2k+1 , make substantial progress on the evaluation of c 5,2k+1 , s 6,2k+1 and t 6,2k+1 and report more limited progress regarding c 5,2k , c 6,2k+1 and c 6,2k . In the process, we obtain eight conjectural evaluations, each of which has been checked to 1200 decimal places. One of these lies deep in four-dimensional quantum field theory and two are probably provable by delicate combinatorics. There remains a hard core of five conjectures whose proofs would be most instructive, to mathematicians and physicists alike

Holographic Formation of Diffraction Elements for Transformation of Light Beams in Liquid Crystal - Photopolymer Compositions

Science.gov (United States)

Semkin, A. O.; Sharangovich, S. N.

2018-03-01

A theoretical model of holographic formation of diffractive optical elements for transformation of light beam field into Bessel-like fields in liquid crystal - photopolymer (LC-PPM) composite materials with a dyesensitizer is developed. Results of numerical modeling of kinetics ofvariation of the refractive index of a material in the process of formation with different relationships between the photopolymerization rates and diffusion processes are presented. Based on the results of numerical simulation, it is demonstrated that when the photopolarization process dominates, the diffractive element being formed is distorted. This leads to a change in the light field distribution at its output and consequently, to ineffective transformation of the reading beam. Thus, the necessity of optimizing of the recording conditions and of the prepolymeric composition to increase the transformation efficiency of light beam fields is demonstrated.

Transducers and arrays for underwater sound

CERN Document Server

Butler, John L

2016-01-01

This improved and updated second edition covers the theory, development, and design of electro-acoustic transducers for underwater applications. This highly regarded text discusses the basics of piezoelectric and magnetostrictive transducers that are currently being used as well as promising new designs. It presents the basic acoustics as well as the specific acoustics data needed in transducer design and evaluation. A broad range of designs of projectors and hydrophones are described in detail along with methods of modeling, evaluation, and measurement. Analysis of projector and hydrophone transducer arrays, including the effects of mutual radiation impedance and numerical models for elements and arrays, are also covered. The book includes new advances in transducer design and transducer materials and has been completely reorganized to be suitable for use as a textbook, as well as a reference or handbook. The new edition contains updates to the first edition, end-of-chapter exercises, and solutions to select...

An enzyme logic bioprotonic transducer

Energy Technology Data Exchange (ETDEWEB)

Miyake, Takeo; Keene, Scott; Deng, Yingxin; Rolandi, Marco, E-mail: rolandi@uw.edu [Department of Materials Science and Engineering, University of Washington, Seattle, Washington 98195-2120 (United States); Josberger, Erik E. [Department of Materials Science and Engineering, University of Washington, Seattle, Washington 98195-2120 (United States); Department of Electrical Engineering, University of Washington, Seattle, Washington 98195-2500 (United States)

2015-01-01

Translating ionic currents into measureable electronic signals is essential for the integration of bioelectronic devices with biological systems. We demonstrate the use of a Pd/PdH{sub x} electrode as a bioprotonic transducer that connects H{sup +} currents in solution into an electronic signal. This transducer exploits the reversible formation of PdH{sub x} in solution according to PdH↔Pd + H{sup +} + e{sup −}, and the dependence of this formation on solution pH and applied potential. We integrate the protonic transducer with glucose dehydrogenase as an enzymatic AND gate for glucose and NAD{sup +}. PdH{sub x} formation and associated electronic current monitors the output drop in pH, thus transducing a biological function into a measurable electronic output.

An exactly solvable model of an oscillator with nonlinear coupling and zeros of Bessel functions

Science.gov (United States)

Dodonov, V. V.; Klimov, A. B.

1993-01-01

We consider an oscillator model with nonpolynomial interaction. The model admits exact solutions for two situations: for energy eigenvalues in terms of zeros of Bessel functions, that were considered as functions of the continuous index; and for the corresponding eigenstates in terms of Lommel polynomials.

A ring transducer system for medical ultrasound research.

Science.gov (United States)

Waag, Robert C; Fedewa, Russell J

2006-10-01

An ultrasonic ring transducer system has been developed for experimental studies of scattering and imaging. The transducer consists of 2048 rectangular elements with a 2.5-MHz center frequency, a 67% -6 dB bandwidth, and a 0.23-mm pitch arranged in a 150-mm-diameter ring with a 25-mm elevation. At the center frequency, the element size is 0.30lambda x 42lambda and the pitch is 0.38lambda. The system has 128 parallel transmit channels, 16 parallel receive channels, a 2048:128 transmit multiplexer, a 2048:16 receive multiplexer, independently programmable transmit waveforms with 8-bit resolution, and receive amplifiers with time variable gain independently programmable over a 40-dB range. Receive signals are sampled at 20 MHz with 12-bit resolution. Arbitrary transmit and receive apertures can be synthesized. Calibration software minimizes system nonidealities caused by noncircularity of the ring and element-to-element response differences. Application software enables the system to be used by specification of high-level parameters in control files from which low-level hardware-dependent parameters are derived by specialized code. Use of the system is illustrated by producing focused and steered beams, synthesizing a spatially limited plane wave, measuring angular scattering, and forming b-scan images.

Certain new unified integrals associated with the product of generalized Bessel functions

Directory of Open Access Journals (Sweden)

Praveen Agarwal

2016-02-01

Full Text Available Our focus to presenting two very general integral formulas whose integrands are the integrand given in the Oberhettinger's integral formula and a finite product of the generalized Bessel function of the first kind, which are expressed in terms of the generalized Lauricella functions. Among a large number of interesting and potentially useful special cases of our main results, some integral formulas involving such elementary functions are also considered.

A note on a hyper-cubic Mahler measure and associated Bessel integral

International Nuclear Information System (INIS)

Glasser, M L

2012-01-01

The Mahler measure for the n-variable polynomial k + ∑(x j + 1/x j ) is reduced to a single integral of the n-th power of the modified Bessel function I 0 . Several special cases are examined in detail. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday. (paper)

Micromachined Ultrasonic Transducers for 3-D Imaging

DEFF Research Database (Denmark)

Christiansen, Thomas Lehrmann

of state-of-the-art 3-D ultrasound systems. The focus is on row-column addressed transducer arrays. This previously sparsely investigated addressing scheme offers a highly reduced number of transducer elements, resulting in reduced transducer manufacturing costs and data processing. To produce...... such transducer arrays, capacitive micromachined ultrasonic transducer (CMUT) technology is chosen for this project. Properties such as high bandwidth and high design flexibility makes this an attractive transducer technology, which is under continuous development in the research community. A theoretical...... treatment of CMUTs is presented, including investigations of the anisotropic plate behaviour and modal radiation patterns of such devices. Several new CMUT fabrication approaches are developed and investigated in terms of oxide quality and surface protrusions, culminating in a simple four-mask process...

Supported silver clusters as nanoplasmonic transducers for protein sensing

DEFF Research Database (Denmark)

Fojan, Peter; Hanif, Muhammad; Bartling, Stephen

2015-01-01

Transducers for optical sensing of proteins are prepared using cluster beam deposition on quartz substrates. Surface plasmon resonance phenomenon of the supported silver clusters is used for the detection. It is shown that surface immobilisation procedure providing adhesion of the silver clusters...... stages and protein immobilisation scheme the sensing of protein of interest can be assured using a relatively simple optical spectroscopy method....... an enhancement of the plasmon absorption band used for the detection. Atomic force microscopy study allows to suggest that immobilisation of antibodies on silver clusters has been achieved, thus giving a possibility to incubate and detect an antigen of interest. Hence, by applying the developed preparation...

Stabilization of synchrotron radiation x-ray beam by MOSTAB

CERN Document Server

Kudo, T P; Tanida, H; Furukawa, Y; Hirono, T; Ishikawa, T; Nishino, Y

2003-01-01

Monochromator stabilization (MOSTAB) is a feedback control system to stabilize an x-ray beam of synchrotron radiation. It applies a feedback voltage to a piezo electric transducer attached to a double-crystal monochromator. We developed MOSTAB modules and examined their performances using SPring-8 beamlines. The x-ray beam position stabilization using MOSTAB was realized simultaneously with the x-ray beam intensity stabilization. As an example of its application, we performed EXAFS measurement with MOSTAB. (author)

Parameter sensitivity study of a Field II multilayer transducer model on a convex transducer

DEFF Research Database (Denmark)

Bæk, David; Jensen, Jørgen Arendt; Willatzen, Morten

2009-01-01

A multilayer transducer model for predicting a transducer impulse response has in earlier works been developed and combined with the Field II software. This development was tested on current, voltage, and intensity measurements on piezoceramics discs (Bæk et al. IUS 2008) and a convex 128 element...... ultrasound imaging transducer (Bæk et al. ICU 2009). The model benefits from its 1D simplicity and hasshown to give an amplitude error around 1.7‐2 dB. However, any prediction of amplitude, phase, and attenuation of pulses relies on the accuracy of manufacturer supplied material characteristics, which may...... is a quantitative calibrated model for a complete ultrasound system. This includes a sensitivity study aspresented here.Statement of Contribution/MethodsThe study alters 35 different model parameters which describe a 128 element convex transducer from BK Medical Aps. The changes are within ±20 % of the values...

Using Portable Transducers to Measure Tremor Severity

Directory of Open Access Journals (Sweden)

Rodger Elble

2016-05-01

Full Text Available Background: Portable motion transducers, suitable for measuring tremor, are now available at a reasonable cost. The use of these transducers requires knowledge of their limitations and data analysis. The purpose of this review is to provide a practical overview and example software for using portable motion transducers in the quantification of tremor. Methods: Medline was searched via PubMed.gov in December 2015 using the Boolean expression “tremor AND (accelerometer OR accelerometry OR gyroscope OR inertial measurement unit OR digitizing tablet OR transducer.” Abstracts of 419 papers dating back to 1964 were reviewed for relevant portable transducers and methods of tremor analysis, and 105 papers written in English were reviewed in detail. Results: Accelerometers, gyroscopes, and digitizing tablets are used most commonly, but few are sold for the purpose of measuring tremor. Consequently, most software for tremor analysis is developed by the user. Wearable transducers are capable of recording tremor continuously, in the absence of a clinician. Tremor amplitude, frequency, and occurrence (percentage of time with tremor can be computed. Tremor amplitude and occurrence correlate strongly with clinical ratings of tremor severity. Discussion: Transducers provide measurements of tremor amplitude that are objective, precise, and valid, but the precision and accuracy of transducers are mitigated by natural variability in tremor amplitude. This variability is so great that the minimum detectable change in amplitude, exceeding random variability, is comparable for scales and transducers. Research is needed to determine the feasibility of detecting smaller change using averaged data from continuous long-term recordings with wearable transducers.

Factorization of products of discontinuous functions applied to Fourier-Bessel basis.

Science.gov (United States)

Popov, Evgeny; Nevière, Michel; Bonod, Nicolas

2004-01-01

The factorization rules of Li [J. Opt. Soc. Am. A 13, 1870 (1996)] are generalized to a cylindrical geometry requiring the use of a Bessel function basis. A theoretical study confirms the validity of the Laurent rule when a product of two continuous functions or of one continuous and one discontinuous function is factorized. The necessity of applying the so-called inverse rule in factorizing a continuous product of two discontinuous functions in a truncated basis is demonstrated theoretically and numerically.

Measurement of a beam equilibrium orbit in the NAP-M storage ring

International Nuclear Information System (INIS)

Zagorodnikov, E.I.; Kalinin, A.S.; Medvedko, A.S.

1976-01-01

The equipment for measurement of the beam equilibrium orbit position in the NAP-M accumulator is described. The measurements are taken by the electrostatic transducers. The signals are delivered from the transducer electrodes to the source followers. At the output of the followers the signals are subtracted by the transformer with a volumetric coil. The total signal is picked off the common load of the followers. The further processing of the total and differential signals is performed with the 1st beam frequency harmonic and consists in rating of the differential signal for the beam current with subsequent synchronous detection. For discrimination of the 1st harmonic, a frequency converter employing field transistors has been designed. The problem of the increasing the accuracy of coincidence of the transmitter electric and geometric centers is discussed. The measuring system operates at the number of the particles on the orbit amounting to (1-2)x10 9 and the beam revesal frequency band within 0.36 - 2.5 MHz. The system has the beam displacement resolution of about 1 mm

Microhydraulic transducer technology for actuation and power generation

Science.gov (United States)

Hagood, Nesbitt W.; Roberts, David C.; Saggere, Laxminarayana; Breuer, Kenneth S.; Chen, Kuo-Shen; Carretero, Jorge A.; Li, Hanqing; Mlcak, Richard; Pulitzer, Seward W.; Schmidt, Martin A.; Spearing, S. Mark; Su, Yu-Hsuan

2000-06-01

The paper introduces a novel transducer technology, called the solid-state micro-hydraulic transducer, currently under development at MIT. The new technology is enabled through integration of micromachining technology, piezoelectrics, and microhydraulic concepts. These micro-hydraulic transducers are capable of bi-directional electromechanical energy conversion, i.e., they can operate as both an actuator that supplies high mechanical force in response to electrical input and an energy generator that transduces electrical energy from mechanical energy in the environment. These transducers are capable of transducing energy at very high specific power output in the order of 1 kW/kg, and thus, they have the potential to enable many novel applications. The concept, the design, and the potential applications of the transducers are presented. Present efforts towards the development of these transducers, and the challenges involved therein, are also discussed.

On the evaluation of modified Bessel functions of the second kind and fractional order for synchrotron radiation calculations

International Nuclear Information System (INIS)

Rutt, H.N.

2003-01-01

The modified Bessel functions of the second kind and fractional order K 1/3 (x) and K 2/3 (x) are of importance in the calculation of the frequency spectrum of synchrotron radiation. The parameter range of interest is typically 10 -6 x10. Recently, there has been particular interest in the generation of 'terahertz' radiation, which can be coherently enhanced by many orders of magnitude when the electron bunch length is shorter than the terahertz wavelength. This requires evaluation of the Bessel functions for small values of the argument. It is shown that the series commonly used to evaluate these functions has poor convergence properties under these conditions. An alternative series is derived which has much better convergence for x1

Capacitive pressure transducer using flexible films. Junan film wo mochiita seiden yoryoshiki atsukaku transducer

Energy Technology Data Exchange (ETDEWEB)

Yamada, Y.; Tsuchida, N.; Imai, K. (Toyota Technological Institute, Aichi (Japan)); Fujita, K. (Nitto Denko Corp., Osaka (Japan)): Tsuboi, O. (Fujitsu Corp., Tokyo (Japan))

1992-12-20

This paper describes the design, manufacture, and evaluation of a capacitive pressure transducer made of polyimide films. The structure of a pressure transducer cell was first determined, and then, the deflection-stress and capacitance-load characteristics of the surface film were analyzed using finite element methods. For the practical stage of manufacture, a polyimide film was emboss processed and electrodes were deposited on the film to construct a pressure transducer cell to which a Schmidt-trigger detecting circuit was connected. As a consequence of the examination of operational characteristics of the cell, it was found that the actual relation between the deflection and load approximately agreed with the linear analyses, and that the capacitance depended with little hysteresis on the gap regardless of the native visco-elasticity of the film. Furthermore, small stick-slip vibration of a contact rubber surface was detected by the transducer to verify its high sensitivity. 17 refs., 18 figs.

Propagation and wavefront ambiguity of linear nondiffracting beams

Science.gov (United States)

Grunwald, R.; Bock, M.

2014-02-01

Ultrashort-pulsed Bessel and Airy beams in free space are often interpreted as "linear light bullets". Usually, interconnected intensity profiles are considered a "propagation" along arbitrary pathways which can even follow curved trajectories. A more detailed analysis, however, shows that this picture gives an adequate description only in situations which do not require to consider the transport of optical signals or causality. To also cover these special cases, a generalization of the terms "beam" and "propagation" is necessary. The problem becomes clearer by representing the angular spectra of the propagating wave fields by rays or Poynting vectors. It is known that quasi-nondiffracting beams can be described as caustics of ray bundles. Their decomposition into Poynting vectors by Shack-Hartmann sensors indicates that, in the frame of their classical definition, the corresponding local wavefronts are ambiguous and concepts based on energy density are not appropriate to describe the propagation completely. For this reason, quantitative parameters like the beam propagation factor have to be treated with caution as well. For applications like communication or optical computing, alternative descriptions are required. A heuristic approach based on vector field based information transport and Fourier analysis is proposed here. Continuity and discontinuity of far field distributions in space and time are discussed. Quantum aspects of propagation are briefly addressed.

Spherical Bessel functions jsub(n) and ysub(n) of integer order and real argument

International Nuclear Information System (INIS)

Ardill, R.W.B.; Moriarty, K.J.M.

1978-01-01

The spherical Bessel function appears in a variety of physical applications, and especially in phase shift analysis. The package SPHBES contains a subroutine to calculate jsub(n)(x) and ysub(n)(x) for any integer order n and real argument x. The functions jsub(n)(x) and ysub(n)(x) are produced simultaneously and efficiently. (Auth.)

A 1372-element Large Scale Hemispherical Ultrasound Phased Array Transducer for Noninvasive Transcranial Therapy

International Nuclear Information System (INIS)

Song, Junho; Hynynen, Kullervo

2009-01-01

Noninvasive transcranial therapy using high intensity focused ultrasound transducers has attracted high interest as a promising new modality for the treatments of brain related diseases. We describe the development of a 1372 element large scale hemispherical ultrasound phased array transducer operating at a resonant frequency of 306 kHz. The hemispherical array has a diameter of 31 cm and a 15.5 cm radius of curvature. It is constructed with piezoelectric (PZT-4) tube elements of a 10 mm in diameter, 6 mm in length and 1.4 mm wall thickness. Each element is quasi-air backed by attaching a cork-rubber membrane on the back of the element. The acoustic efficiency of the element is determined to be approximately 50%. The large number of the elements delivers high power ultrasound and offers better beam steering and focusing capability. Comparisons of sound pressure-squared field measurements with theoretical calculations in water show that the array provides good beam steering and tight focusing capability over an efficient volume of approximately 100x100x80 mm 3 with nominal focal spot size of approximately 2.3 mm in diameter at -6 dB. We also present its beam steering and focusing capability through an ex vivo human skull by measuring pressure-squared amplitude after phase corrections. These measurements show the same efficient volume range and focal spot sizes at -6 dB as the ones in water without the skull present. These results indicate that the array is sufficient for use in noninvasive transcranial ultrasound therapy.

Theory and experiment of Fourier-Bessel field calculation and tuning of a pulsed wave annular array

DEFF Research Database (Denmark)

Fox, Paul D.; Jiqi, Cheng; Jian-yu, Lu

2003-01-01

A one-dimensional (1D) Fourier-Bessel series method for computing and tuning (beamforming) the linear lossless field of flat pulsed wave annular arrays is developed and supported with both numerical simulation and experimental verification. The technique represents a new method for modeling and t...

Coaxial Transducer

National Research Council Canada - National Science Library

Ruffa, Anthony A

2008-01-01

The invention as disclosed is of a coaxial transducer that uses lead zirconate titanate ceramic or other suitable material as an isolator between the conductors in a coaxial cable to transmit acoustic...

Entangled Bessel-Gaussian beams

CSIR Research Space (South Africa)

McLaren, M

2012-10-01

Full Text Available by performing a Bell-type experiment and showing a violation of the Clauser-Horne-Shimony-Holt inequality. In addition, we use quantum state tomography to indicate higher-dimensional entanglement in terms of BG modes....

Unravelling Bessel beams: Presentation

CSIR Research Space (South Africa)

Mhlanga, T

2013-07-01

Full Text Available Mhlanga1,3, Angela Dudley1, Martin Lavery2, Miles Padgett2 and Andrew Forbes1,3 1CSIR National Laser Centre, PO Box 395, Pretoria, 0001, South Africa 2Department of Physics & Astronomy, University of Glasgow, Glasgow, UK 3College of Agriculture...,* Thandeka Mhlanga,1Martin Lavery,2 Andre McDonald,1 Filippus S. Roux,1 Miles Padgett,2 and Andrew Forbes1 1CSIR National Laser Centre, PO Box 395, Pretoria 0001, South Africa 2 Department of Physics & Astronomy, University of Glasgow, Glasgow, UK *adudley...

Fourier Bessel transform method for efficiently calculating the magnetic field of solenoids

International Nuclear Information System (INIS)

Nachamkin, J.; Maggiore, C.J.

1980-01-01

A numerical procedure for calculating the magnetic field of a selenoid is derived. Based on the properties of Bessel functions, the procedure is shown to be convergent everywhere, including within the windings of the solenoid. The most critical part of the procedure is detailed in the main text. A simple method is used to ensure numerical significance while allowing economical computational times. In the appendix the procedure is generalized to universal convergence by appropriate partitioning of the solenoid windings

High resolution multiplexed functional imaging in live embryos (Conference Presentation)

Science.gov (United States)

Xu, Dongli; Zhou, Weibin; Peng, Leilei

2017-02-01

Fourier multiplexed fluorescence lifetime imaging (FmFLIM) scanning laser optical tomography (FmFLIM-SLOT) combines FmFLIM and Scanning laser optical tomography (SLOT) to perform multiplexed 3D FLIM imaging of live embryos. The system had demonstrate multiplexed functional imaging of zebrafish embryos genetically express Foster Resonant Energy Transfer (FRET) sensors. However, previous system has a 20 micron resolution because the focused Gaussian beam diverges quickly from the focused plane, makes it difficult to achieve high resolution imaging over a long projection depth. Here, we present a high-resolution FmFLIM-SLOT system with achromatic Bessel beam, which achieves 3 micron resolution in 3D deep tissue imaging. In Bessel-FmFLIM-SLOT, multiple laser excitation lines are firstly intensity modulated by a Michelson interferometer with a spinning polygon mirror optical delay line, which enables Fourier multiplexed multi-channel lifetime measurements. Then, a spatial light modulator and a prism are used to transform the modulated Gaussian laser beam to an achromatic Bessel beam. The achromatic Bessel beam scans across the whole specimen with equal angular intervals as sample rotated. After tomography reconstruction and the frequency domain lifetime analysis method, both the 3D intensity and lifetime image of multiple excitation-emission can be obtained. Using Bessel-FmFLIM-SLOT system, we performed cellular-resolution FLIM tomography imaging of live zebrafish embryo. Genetically expressed FRET sensors in these embryo will allow non-invasive observation of multiple biochemical processes in vivo.

The Dynamic Performance of Flexural Ultrasonic Transducers

Directory of Open Access Journals (Sweden)

Andrew Feeney

2018-01-01

Full Text Available Flexural ultrasonic transducers are principally used as proximity sensors and for industrial metrology. Their operation relies on a piezoelectric ceramic to generate a flexing of a metallic membrane, which delivers the ultrasound signal. The performance of flexural ultrasonic transducers has been largely limited to excitation through a short voltage burst signal at a designated mechanical resonance frequency. However, a steady-state amplitude response is not generated instantaneously in a flexural ultrasonic transducer from a drive excitation signal, and differences in the drive characteristics between transmitting and receiving transducers can affect the measured response. This research investigates the dynamic performance of flexural ultrasonic transducers using acoustic microphone measurements and laser Doppler vibrometry, supported by a detailed mechanical analog model, in a process which has not before been applied to the flexural ultrasonic transducer. These techniques are employed to gain insights into the physics of their vibration behaviour, vital for the optimisation of industrial ultrasound systems.

Non-Compact and Sharp Embeddings of Logarithmic Bessel Potential Spaces into Hölder-Type Spaces

Czech Academy of Sciences Publication Activity Database

Edmunds, D. E.; Gurka, P.; Opic, Bohumír

2006-01-01

Roč. 25, č. 1 (2006), s. 73-80 ISSN 0232-2064 R&D Projects: GA ČR(CZ) GA201/01/0333 Institutional research plan: CEZ:AV0Z10190503 Keywords : generalized Lorentz-Zygmund spaces * logarithmic Bessel potential spaces * Hölder-continuous functions Subject RIV: BA - General Mathematics Impact factor: 0.360, year: 2006

Linear Array Ultrasonic Transducers: Sensitivity and Resolution Study

International Nuclear Information System (INIS)

Kramb, V.A.

2005-01-01

The University of Dayton Research Institute (UDRI) under contract by the US Air Force has designed and integrated a fully automated inspection system for the inspection of turbine engines that incorporates linear phased array ultrasonic transducers. Phased array transducers have been successfully implemented into weld and turbine blade root inspections where the defect types are well known and characterized. Embedded defects in aerospace turbine engine components are less well defined, however. In order to determine the applicability of linear arrays to aerospace inspections the sensitivity of array transducers to embedded defects in engine materials must be characterized. In addition, the implementation of array transducers into legacy inspection procedures must take into account any differences in sensitivity between the array transducer and that of the single element transducer currently used. This paper discusses preliminary results in a study that compares the sensitivity of linear array and conventional single element transducers to synthetic hard alpha defects in a titanium alloy

Accurate Bessel functions Jsub(n)(z), Ysub(n)(z), Hsub(n)sup((1))(z) and Hsub(n)sup((2))(z) of integer order and complex argument

International Nuclear Information System (INIS)

Ardill, R.W.B.; Moriarty, K.J.M.

1979-01-01

The Bessel function appears in a wide range of physical applications, and in particular where there is axial symmetry. The package contains complex function routines to calculate Jsub(n)(z), Ysub(n)(z), Hsub(n)sup((1))(z) and Hsub(n)sup((2))(z) for integer n and complex z. The method of solution is based on the ascending series representations and asymptotic forms of the Bessel functions Jsub(n)(z) and Ysub(n)(z) and asymptotic forms of the modified Bessel functions Isub(n)(z) and Ksub(n)(z). The program will return results for all values of mod(z) up to machine overflows in the Bessel functions. The size of the order should not be too large (say, mod(n) -11 . For the asymptotic region, the accuracy EPS may not always be achieved (since the asymptotic series may have to be truncated at their lower terms), in which case the output parameter ISET will indicate this and an estimation of the relative error is also produced. The functions Ysub(n)(z), Hsub(n)sup((1))(z) and Hsub(n)sup((2))(z) have a branch point at the origin, together with a cut along the negative real axis. (Auth.)

Ultrasonic properties of all-printed piezoelectric polymer transducers

Science.gov (United States)

Wagle, Sanat; Decharat, Adit; Bodö, Peter; Melandsø, Frank

2013-12-01

The ability of producing ultrasonic transducers from screen-printing has been explored experimentally, through printing and characterization of a large number of transducers. In an all-printed test design, 124 transducers with four different electrode sizes ranging from 1 to 4.9 mm2, were printed layer-by-layer on a high performance polyethyleneimine polymer. Inks from ferroelectric and conductive polymers were applied to the active part of a transducer, to provide a good acoustical match between the individual layers. Ultrasonic characterizations of the transducers done by two independent methods provided a broad-banded frequency response with a maximum response around 100 MHz.

Mechanism of nanosecond laser drilling process of 4H-SiC for through substrate vias

Science.gov (United States)

Kim, Byunggi; Iida, Ryoichi; Doan, Duc Hong; Fushinobu, Kazuyoshi

2017-06-01

Role of optical parameters on nanosecond laser drilling of 4H-SiC was experimentally studied. Using ns pulsed Nd:YAG laser, parametric studies on effects of wavelength (1064 nm or 532 nm), beam profile (Gaussian or Bessel), and ambient condition (air or water) were conducted. The wavelengths which have large optical penetration depth were selected as wavefront has to propagate through materials to generate Bessel beam. The experimental results showed that carbonization of SiC surface accelerates thermal ablation of the materials with fluence under the lattice melting threshold. Especially, pattern of side lobes with small fluence was formed by irradiation of Bessel beam. The pattern disturbed penetration of wavefronts through materials. Implementation of water environment was not effective to suppress carbonization and had slight effect on improvement of drilling quality. For this reason, deep drilling with small entrance was not achieved using Bessel beam. Irradiation of 1064 nm Gaussian beam with large fluence led to formation of critical amount of re-solidified silicon due to the large optical penetration depth. Carbonization and silicon formation had a significant effect on unique fluence dependence of drilling depth. Absorption mechanism was studied as well to discuss effect of wavelength on processing characteristics.

The research on high power transducer

International Nuclear Information System (INIS)

Zhao Wuling; Li Yubin; Peng Shuwen

2014-01-01

This paper introduces the transducer structure used double PWM mode, the control system design of hardware and software. The transducer has been applied in factory. From the real experiment, it shows that the system has a high reliability. (authors)

Nonlinear focal shift beyond the geometrical focus in moderately focused acoustic beams.

Science.gov (United States)

Camarena, Francisco; Adrián-Martínez, Silvia; Jiménez, Noé; Sánchez-Morcillo, Víctor

2013-08-01

The phenomenon of the displacement of the position along the axis of the pressure, intensity, and radiation force maxima of focused acoustic beams under increasing driving voltages (nonlinear focal shift) is studied for the case of a moderately focused beam. The theoretical and experimental results show the existence of this shift along the axis when the initial pressure in the transducer increases until the acoustic field reaches the fully developed nonlinear regime of propagation. Experimental data show that at high amplitudes and for moderate focusing, the position of the on-axis pressure maximum and radiation force maximum can surpass the geometrical focal length. On the contrary, the on-axis pressure minimum approaches the transducer under increasing driving voltages, increasing the distance between the positive and negative peak pressure in the beam. These results are in agreement with numerical KZK model predictions and the existed data of other authors and can be explained according to the effect of self-refraction characteristic of the nonlinear regime of propagation.

Using axicons for depth discrimination in excitation-emission laser scanning imaging systems

Science.gov (United States)

Iglesias, Ignacio

2017-10-01

Besides generating good approximations to zero-order Bessel beams, an axicon lens coupled to a spatial filter can be used to collect light while preserving information on the depth coordinate of the source location. To demonstrate the principle, we describe an experimental excitation-emission fluorescence imaging system that uses an axicon twice: to generate an excitation Bessel beam and to collect the emitted light.

On the propagation of transient waves in a viscoelastic Bessel medium

Science.gov (United States)

Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco

2017-06-01

In this paper, we discuss the uniaxial propagation of transient waves within a semi-infinite viscoelastic Bessel medium. First, we provide the analytic expression for the response function of the material as we approach the wave front. To do so, we take profit of a revisited version of the so called Buchen-Mainardi algorithm. Secondly, we provide an analytic expression for the long-time behavior of the response function of the material. This result is obtained by means of the Tauberian theorems for the Laplace transform. Finally, we relate the obtained results to a peculiar model for fluid-filled elastic tubes.

Nano-optomechanical transducer

Science.gov (United States)

Rakich, Peter T; El-Kady, Ihab F; Olsson, Roy H; Su, Mehmet Fatih; Reinke, Charles; Camacho, Ryan; Wang, Zheng; Davids, Paul

2013-12-03

A nano-optomechanical transducer provides ultrabroadband coherent optomechanical transduction based on Mach-wave emission that uses enhanced photon-phonon coupling efficiencies by low impedance effective phononic medium, both electrostriction and radiation pressure to boost and tailor optomechanical forces, and highly dispersive electromagnetic modes that amplify both electrostriction and radiation pressure. The optomechanical transducer provides a large operating bandwidth and high efficiency while simultaneously having a small size and minimal power consumption, enabling a host of transformative phonon and signal processing capabilities. These capabilities include optomechanical transduction via pulsed phonon emission and up-conversion, broadband stimulated phonon emission and amplification, picosecond pulsed phonon lasers, broadband phononic modulators, and ultrahigh bandwidth true time delay and signal processing technologies.

Beam pattern improvement by compensating array nonuniformities in a guided wave phased array

International Nuclear Information System (INIS)

Kwon, Hyu-Sang; Lee, Seung-Seok; Kim, Jin-Yeon

2013-01-01

This paper presents a simple data processing algorithm which can improve the performance of a uniform circular array based on guided wave transducers. The algorithm, being intended to be used with the delay-and-sum beamformer, effectively eliminates the effects of nonuniformities that can significantly degrade the beam pattern. Nonuniformities can arise intrinsically from the array geometry when the circular array is transformed to a linear array for beam steering and extrinsically from unequal conditions of transducers such as element-to-element variations of sensitivity and directivity. The effects of nonuniformities are compensated by appropriately imposing weight factors on the elements in the projected linear array. Different cases are simulated, where the improvements of the beam pattern, especially the level of the highest sidelobe, are clearly seen, and related issues are discussed. An experiment is performed which uses A0 mode Lamb waves in a steel plate, to demonstrate the usefulness of the proposed method. The discrepancy between theoretical and experimental beam patterns is explained by accounting for near-field effects. (paper)

Average intensity and spreading of partially coherent model beams propagating in a turbulent biological tissue

International Nuclear Information System (INIS)

Wu, Yuqian; Zhang, Yixin; Wang, Qiu; Hu, Zhengda

2016-01-01

For Gaussian beams with three different partially coherent models, including Gaussian-Schell model (GSM), Laguerre-Gaussian Schell-model (LGSM) and Bessel-Gaussian Schell-model (BGSM) beams propagating through a biological turbulent tissue, the expression of the spatial coherence radius of a spherical wave propagating in a turbulent biological tissue, and the average intensity and beam spreading for GSM, LGSM and BGSM beams are derived based on the fractal model of power spectrum of refractive-index variations in biological tissue. Effects of partially coherent model and parameters of biological turbulence on such beams are studied in numerical simulations. Our results reveal that the spreading of GSM beams is smaller than LGSM and BGSM beams on the same conditions, and the beam with larger source coherence width has smaller beam spreading than that with smaller coherence width. The results are useful for any applications involved light beam propagation through tissues, especially the cases where the average intensity and spreading properties of the light should be taken into account to evaluate the system performance and investigations in the structures of biological tissue. - Highlights: • Spatial coherence radius of a spherical wave propagating in a turbulent biological tissue is developed. • Expressions of average intensity and beam spreading for GSM, LGSM and BGSM beams in a turbulent biological tissue are derived. • The contrast for the three partially coherent model beams is shown in numerical simulations. • The results are useful for any applications involved light beam propagation through tissues.

Strong-field ionization with twisted laser pulses

Science.gov (United States)

Paufler, Willi; Böning, Birger; Fritzsche, Stephan

2018-04-01

We apply quantum trajectory Monte Carlo computations in order to model strong-field ionization of atoms by twisted Bessel pulses and calculate photoelectron momentum distributions (PEMD). Since Bessel beams can be considered as an infinite superposition of circularly polarized plane waves with the same helicity, whose wave vectors lie on a cone, we compared the PEMD of such Bessel pulses to those of a circularly polarized pulse. We focus on the momentum distributions in propagation direction of the pulse and show how these momentum distributions are affected by experimental accessible parameters, such as the opening angle of the beam or the impact parameter of the atom with regard to the beam axis. In particular, we show that we can find higher momenta of the photoelectrons, if the opening angle is increased.

A new high performance current transducer

International Nuclear Information System (INIS)

Tang Lijun; Lu Songlin; Li Deming

2003-01-01

A DC-100 kHz current transducer is developed using a new technique on zero-flux detecting principle. It was shown that the new current transducer is of high performance, its magnetic core need not be selected very stringently, and it is easy to manufacture

The effect of concrete strength and reinforcement on toughness of reinforced concrete beams

OpenAIRE

Carneiro, Joaquim A. O.; Jalali, Said; Teixeira, Vasco M. P.; Tomás, M.

2005-01-01

The objective pursued with this work includes the evaluating of the strength and the total energy absorption capacity (toughness) of reinforced concrete beams using different amounts of steel-bar reinforcement. The experimental campaign deals with the evaluation of the threshold load prior collapse, ultimate load and deformation, as well as the beam total energy absorption capacity, using a three point bending test. The beam half span displacement was measured using a displacement transducer,...

Equivalent circuit models of two-layer flexure beams with excitation by temperature, humidity, pressure, piezoelectric or piezomagnetic interactions

Directory of Open Access Journals (Sweden)

U. Marschner

2014-09-01

Full Text Available Two-layer flexure beams often serve as basic transducers in actuators and sensors. In this paper a generalized description of their stimuli-influenced mechanical behavior is derived. For small deflection angles this description includes a multi-port circuit or network representation with lumped elements for a beam part of finite length. A number of coupled finite beam parts model the dynamic behavior including the first natural frequencies of the beam. For piezoelectric and piezomagnetic interactions, reversible transducer models are developed. The piezomagnetic two-layer beam model is extended to include solenoid and planar coils. Linear network theory is applied in order to determine network parameters and to simplify the circuit representation. The resulting circuit model is the basis for a fast simulation of the dynamic system behavior with advanced circuit simulators and, thus, the optimization of the system. It is also a useful tool for understanding and explaining this multi-domain system through basic principles of general system theory.

Study of Impact Damage in PVA-ECC Beam under Low-Velocity Impact Loading Using Piezoceramic Transducers and PVDF Thin-Film Transducers.

Science.gov (United States)

Qi, Baoxin; Kong, Qingzhao; Qian, Hui; Patil, Devendra; Lim, Ing; Li, Mo; Liu, Dong; Song, Gangbing

2018-02-24

Compared to conventional concrete, polyvinyl alcohol fiber reinforced engineering cementitious composite (PVA-ECC) offers high-strength, ductility, formability, and excellent fatigue resistance. However, impact-induced structural damage is a major concern and has not been previously characterized in PVA-ECC structures. We investigate the damage of PVA-ECC beams under low-velocity impact loading. A series of ball-drop impact tests were performed at different drop weights and heights to simulate various impact energies. The impact results of PVA-ECC beams were compared with mortar beams. A combination of polyvinylidene fluoride (PVDF) thin-film sensors and piezoceramic-based smart aggregate were used for impact monitoring, which included impact initiation and crack evolution. Short-time Fourier transform (STFT) of the signal received by PVDF thin-film sensors was performed to identify impact events, while active-sensing approach was utilized to detect impact-induced crack evolution by the attenuation of a propagated guided wave. Wavelet packet-based energy analysis was performed to quantify failure development under repeated impact tests.

Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions

CERN Document Server

Farrell, Orin J

2013-01-01

Nearly 200 problems, each with a detailed, worked-out solution, deal with the properties and applications of the gamma and beta functions, Legendre polynomials, and Bessel functions. The first two chapters examine gamma and beta functions, including applications to certain geometrical and physical problems such as heat-flow in a straight wire. The following two chapters treat Legendre polynomials, addressing applications to specific series expansions, steady-state heat-flow temperature distribution, gravitational potential of a circular lamina, and application of Gauss's mechanical quadrature

The application of a Bessel transform to the determination of stellar rotational velocities

International Nuclear Information System (INIS)

Deeming, T.J.

1977-01-01

A method for analysing line profiles by means of a transform using Bessel functions is described. This yields the stellar rotational velocity γ sin i, to an accuracy of about +-1 km s -1 for rotational velocities greater than about 5 km s -1 , provided that rotation is the major source of line broadening. The theory of the method is a special case of a general theory of linear transforms in data analysis, which is outlined in an appendix. (Auth.)

Steerable Doppler transducer probes

International Nuclear Information System (INIS)

Fidel, H.F.; Greenwood, D.L.

1986-01-01

An ultrasonic diagnostic probe is described which is capable of performing ultrasonic imaging and Doppler measurement consisting of: a hollow case having an acoustic window which passes ultrasonic energy and including chamber means for containing fluid located within the hollow case and adjacent to a portion of the acoustic window; imaging transducer means, located in the hollow case and outside the fluid chamber means, and oriented to direct ultrasonic energy through the acoustic window toward an area which is to be imaged; Doppler transducer means, located in the hollow case within the fluid chamber means, and movably oriented to direct Doppler signals through the acoustic window toward the imaged area; means located within the fluid chamber means and externally controlled for controllably moving the Doppler transducer means to select one of a plurality of axes in the imaged area along which the Doppler signals are to be directed; and means, located external to the fluid chamber means and responsive to the means for moving, for providing an indication signal for identifying the selected axis

All-optical optoacoustic microscopy based on probe beam deflection technique

OpenAIRE

Maswadi, Saher M.; Ibey, Bennett L.; Roth, Caleb C.; Tsyboulski, Dmitri A.; Beier, Hope T.; Glickman, Randolph D.; Oraevsky, Alexander A.

2016-01-01

Optoacoustic (OA) microscopy using an all-optical system based on the probe beam deflection technique (PBDT) for detection of laser-induced acoustic signals was investigated as an alternative to conventional piezoelectric transducers. PBDT provides a number of advantages for OA microscopy including (i) efficient coupling of laser excitation energy to the samples being imaged through the probing laser beam, (ii) undistorted coupling of acoustic waves to the detector without the need for separa...

A LVDT conditioner for the beam profile monitors of the AmPS

International Nuclear Information System (INIS)

Es, J.T. van; Trigt, J.H. van.

1991-01-01

A LVDT (Linear Variable Differential Transformer) is a transducer for localization. Because of its applied materials, its construction and the absence of bearings etc. the instrument is suitable to be applied in locations where radioactive radiation is present. In order to obtain information about the position of the iron core in the transducer, a conditioner is needed. In 1977 by Digel a conditioner has been developed for the beam profile monitors (moving wire) of MEA because the 'market' could not meet the requirements then. Nowadays the 'market' offers i.c.'s which can take over the work of the Eurocard developed then. Digel has investigated them in order to see if they are applicable for the beam profile monitors of AmPS. (author). 5 refs.; 7 figs.; 13 tabs

Reflection and transmission of full-vector X-waves normally incident on dielectric half spaces

KAUST Repository

Salem, Mohamed; Bagci, Hakan

2011-01-01

polarization components, which are derived from the scalar X-Wave solution. The analysis of transmission and reflection is carried out via a straightforward but yet effective method: First, the X-Wave is decomposed into vector Bessel beams via the Bessel-Fourier

Transducers for Sound and Vibration - FEM Based Design

DEFF Research Database (Denmark)

Liu, Bin

2001-01-01

Design of transducers for measurement of vibration (piezoelectric accelerometers) and sound (condenser microphones) is a very labour intensive work. The design work is mostly based on experience and on simple analogies to electrical circuit design. Often a time consuming itterative loop is used......: Specification of the transducer, production of a physical prototype, measurements on the prototype, changed specification of the transducer etc. Furthermore are many transducers made based on customer requirements which also increases the amount of required design work. For these reasons there is a need...... for methods that can reduce the design time consumption and the number of itterations. The present work proposes to use finite element based programs for simulating the behaviour of a transducer with a given set of specifications. A simulation program for accelerometers was developed and has been tested...

A Generalized Dynamic Composition Algorithm of Weighted Finite State Transducers for Large Vocabulary Speech Recognition

OpenAIRE

Cheng, Octavian; Dines, John; Magimai.-Doss, Mathew

2006-01-01

We propose a generalized dynamic composition algorithm of weighted finite state transducers (WFST), which avoids the creation of non-coaccessible paths, performs weight look-ahead and does not impose any constraints to the topology of the WFSTs. Experimental results on Wall Street Journal (WSJ1) 20k-word trigram task show that at 17\\% WER (moderately-wide beam width), the decoding time of the proposed approach is about 48\\% and 65\\% of the other two dynamic composition approaches. In comparis...

SU-G-JeP3-03: Effect of Robot Pose On Beam Blocking for Ultrasound Guided SBRT of the Prostate

Energy Technology Data Exchange (ETDEWEB)

Gerlach, S; Schlaefer, A [Hamburg University of Technology, Hamburg (Germany); Kuhlemann, I; Ernst, F [Universitaet zu Luebeck, Luebeck (Germany); Fuerweger, C [European Cyberknife Center Munich, Munich (Germany)

2016-06-15

Purpose: Ultrasound presents a fast, volumetric image modality for real-time tracking of abdominal organ motion. How-ever, ultrasound transducer placement during radiation therapy is challenging. Recently, approaches using robotic arms for intra-treatment ultrasound imaging have been proposed. Good and reliable imaging requires placing the transducer close to the PTV. We studied the effect of a seven degrees of freedom robot on the fea-sible beam directions. Methods: For five CyberKnife prostate treatment plans we established viewports for the transducer, i.e., points on the patient surface with a soft tissue view towards the PTV. Choosing a feasible transducer pose and using the kinematic redundancy of the KUKA LBR iiwa robot, we considered three robot poses. Poses 1 to 3 had the elbow point anterior, superior, and inferior, respectively. For each pose and each beam starting point, the pro-jections of robot and PTV were computed. We added a 20 mm margin accounting for organ / beam motion. The number of nodes for which the PTV was partially of fully blocked were established. Moreover, the cumula-tive overlap for each of the poses and the minimum overlap over all poses were computed. Results: The fully and partially blocked nodes ranged from 12% to 20% and 13% to 27%, respectively. Typically, pose 3 caused the fewest blocked nodes. The cumulative overlap ranged from 19% to 29%. Taking the minimum overlap, i.e., considering moving the robot’s elbow while maintaining the transducer pose, the cumulative over-lap was reduced to 16% to 18% and was 3% to 6% lower than for the best individual pose. Conclusion: Our results indicate that it is possible to identify feasible ultrasound transducer poses and to use the kinematic redundancy of a 7 DOF robot to minimize the impact of the imaging subsystem on the feasible beam directions for ultrasound guided and motion compensated SBRT. Research partially funded by DFG grants ER 817/1-1 and SCHL 1844/3-1.

SU-G-JeP3-03: Effect of Robot Pose On Beam Blocking for Ultrasound Guided SBRT of the Prostate

International Nuclear Information System (INIS)

Gerlach, S; Schlaefer, A; Kuhlemann, I; Ernst, F; Fuerweger, C

2016-01-01

Purpose: Ultrasound presents a fast, volumetric image modality for real-time tracking of abdominal organ motion. How-ever, ultrasound transducer placement during radiation therapy is challenging. Recently, approaches using robotic arms for intra-treatment ultrasound imaging have been proposed. Good and reliable imaging requires placing the transducer close to the PTV. We studied the effect of a seven degrees of freedom robot on the fea-sible beam directions. Methods: For five CyberKnife prostate treatment plans we established viewports for the transducer, i.e., points on the patient surface with a soft tissue view towards the PTV. Choosing a feasible transducer pose and using the kinematic redundancy of the KUKA LBR iiwa robot, we considered three robot poses. Poses 1 to 3 had the elbow point anterior, superior, and inferior, respectively. For each pose and each beam starting point, the pro-jections of robot and PTV were computed. We added a 20 mm margin accounting for organ / beam motion. The number of nodes for which the PTV was partially of fully blocked were established. Moreover, the cumula-tive overlap for each of the poses and the minimum overlap over all poses were computed. Results: The fully and partially blocked nodes ranged from 12% to 20% and 13% to 27%, respectively. Typically, pose 3 caused the fewest blocked nodes. The cumulative overlap ranged from 19% to 29%. Taking the minimum overlap, i.e., considering moving the robot’s elbow while maintaining the transducer pose, the cumulative over-lap was reduced to 16% to 18% and was 3% to 6% lower than for the best individual pose. Conclusion: Our results indicate that it is possible to identify feasible ultrasound transducer poses and to use the kinematic redundancy of a 7 DOF robot to minimize the impact of the imaging subsystem on the feasible beam directions for ultrasound guided and motion compensated SBRT. Research partially funded by DFG grants ER 817/1-1 and SCHL 1844/3-1.

High Temperature, High Power Piezoelectric Composite Transducers

Science.gov (United States)

Lee, Hyeong Jae; Zhang, Shujun; Bar-Cohen, Yoseph; Sherrit, StewarT.

2014-01-01

Piezoelectric composites are a class of functional materials consisting of piezoelectric active materials and non-piezoelectric passive polymers, mechanically attached together to form different connectivities. These composites have several advantages compared to conventional piezoelectric ceramics and polymers, including improved electromechanical properties, mechanical flexibility and the ability to tailor properties by using several different connectivity patterns. These advantages have led to the improvement of overall transducer performance, such as transducer sensitivity and bandwidth, resulting in rapid implementation of piezoelectric composites in medical imaging ultrasounds and other acoustic transducers. Recently, new piezoelectric composite transducers have been developed with optimized composite components that have improved thermal stability and mechanical quality factors, making them promising candidates for high temperature, high power transducer applications, such as therapeutic ultrasound, high power ultrasonic wirebonding, high temperature non-destructive testing, and downhole energy harvesting. This paper will present recent developments of piezoelectric composite technology for high temperature and high power applications. The concerns and limitations of using piezoelectric composites will also be discussed, and the expected future research directions will be outlined. PMID:25111242

Home Automation System Based on Intelligent Transducer Enablers

Science.gov (United States)

Suárez-Albela, Manuel; Fraga-Lamas, Paula; Fernández-Caramés, Tiago M.; Dapena, Adriana; González-López, Miguel

2016-01-01

This paper presents a novel home automation system named HASITE (Home Automation System based on Intelligent Transducer Enablers), which has been specifically designed to identify and configure transducers easily and quickly. These features are especially useful in situations where many transducers are deployed, since their setup becomes a cumbersome task that consumes a significant amount of time and human resources. HASITE simplifies the deployment of a home automation system by using wireless networks and both self-configuration and self-registration protocols. Thanks to the application of these three elements, HASITE is able to add new transducers by just powering them up. According to the tests performed in different realistic scenarios, a transducer is ready to be used in less than 13 s. Moreover, all HASITE functionalities can be accessed through an API, which also allows for the integration of third-party systems. As an example, an Android application based on the API is presented. Remote users can use it to interact with transducers by just using a regular smartphone or a tablet. PMID:27690031

Home Automation System Based on Intelligent Transducer Enablers.

Science.gov (United States)

Suárez-Albela, Manuel; Fraga-Lamas, Paula; Fernández-Caramés, Tiago M; Dapena, Adriana; González-López, Miguel

2016-09-28

This paper presents a novel home automation system named HASITE (Home Automation System based on Intelligent Transducer Enablers), which has been specifically designed to identify and configure transducers easily and quickly. These features are especially useful in situations where many transducers are deployed, since their setup becomes a cumbersome task that consumes a significant amount of time and human resources. HASITE simplifies the deployment of a home automation system by using wireless networks and both self-configuration and self-registration protocols. Thanks to the application of these three elements, HASITE is able to add new transducers by just powering them up. According to the tests performed in different realistic scenarios, a transducer is ready to be used in less than 13 s. Moreover, all HASITE functionalities can be accessed through an API, which also allows for the integration of third-party systems. As an example, an Android application based on the API is presented. Remote users can use it to interact with transducers by just using a regular smartphone or a tablet.

Home Automation System Based on Intelligent Transducer Enablers

Directory of Open Access Journals (Sweden)

Manuel Suárez-Albela

2016-09-01

Full Text Available This paper presents a novel home automation system named HASITE (Home Automation System based on Intelligent Transducer Enablers, which has been specifically designed to identify and configure transducers easily and quickly. These features are especially useful in situations where many transducers are deployed, since their setup becomes a cumbersome task that consumes a significant amount of time and human resources. HASITE simplifies the deployment of a home automation system by using wireless networks and both self-configuration and self-registration protocols. Thanks to the application of these three elements, HASITE is able to add new transducers by just powering them up. According to the tests performed in different realistic scenarios, a transducer is ready to be used in less than 13 s. Moreover, all HASITE functionalities can be accessed through an API, which also allows for the integration of third-party systems. As an example, an Android application based on the API is presented. Remote users can use it to interact with transducers by just using a regular smartphone or a tablet.

Certain fractional integral formulas involving the product of generalized Bessel functions.

Science.gov (United States)

Baleanu, D; Agarwal, P; Purohit, S D

2013-01-01

We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions

Science.gov (United States)

Baleanu, D.; Agarwal, P.; Purohit, S. D.

2013-01-01

We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions. PMID:24379745

Capacitance high temperature strain transducer by Interatom

International Nuclear Information System (INIS)

Fortmann, M.

1987-01-01

Special strain transducers are necessary to perform structure mechanical experiments on real components under creep-fatigue load. The new development of the transducer was able to solve the problem. In the meantime, different characteristics of the transducer have been examined and many successful applications have been effected. Some important aspects are given in this report. Up to now the longest operation period has been 24000 h on a pipe at 630 0 C service temperature in a conventional power station. (orig./DG) [de

High Temperature Ultrasonic Transducer for Real-time Inspection

Science.gov (United States)

Amini, Mohammad Hossein; Sinclair, Anthony N.; Coyle, Thomas W.

A broadband ultrasonic transducer with a novel porous ceramic backing layer is introduced to operate at 700 °C. 36° Y-cut lithium niobate (LiNbO3) single crystal was selected for the piezoelectric element. By appropriate choice of constituent materials, porosity and pore size, the acoustic impedance and attenuation of a zirconia-based backing layer were optimized. An active brazing alloy with high temperature and chemical stability was selected to bond the transducer layers together. Prototype transducers have been tested at temperatures up to 700 °C. The experiments confirmed that transducer integrity was maintained.

Possibility of cellulose-based electro-active paper energy scavenging transducer.

Science.gov (United States)

Abas, Zafar; Kim, Heung Soo; Zhai, Lindong; Kim, Jaehwan; Kim, Joo Hyung

2014-10-01

In this paper, a cellulose-based Electro-Active Paper (EAPap) energy scavenging transducer is presented. Cellulose is proven as a smart material, and exhibits piezoelectric effect. Specimens were prepared by coating gold electrodes on both sides of cellulose film. The fabricated specimens were tested by a base excited aluminum cantilever beam at resonant frequency. Different tests were performed with single and multiple parallel connected electrodes coated on the cellulose film. A maximum of 131 mV output voltage was measured, when three electrodes were connected in parallel. It was observed that voltage output increases significantly with the area of electrodes. From these results, it can be concluded that the piezoelectricity of cellulose-based EAPap can be used in energy transduction application.

Hybrid organic-inorganic porous semiconductor transducer for multi-parameters sensing.

Science.gov (United States)

Caliò, Alessandro; Cassinese, Antonio; Casalino, Maurizio; Rea, Ilaria; Barra, Mario; Chiarella, Fabio; De Stefano, Luca

2015-07-06

Porous silicon (PSi) non-symmetric multi-layers are modified by organic molecular beam deposition of an organic semiconductor, namely the N,N'-1H,1H-perfluorobutyldicyanoperylene-carboxydi-imide (PDIF-CN2). Joule evaporation of PDIF-CN2 into the PSi sponge-like matrix not only improves but also adds transducing skills, making this solid-state device a dual signal sensor for chemical monitoring. PDIF-CN2 modified PSi optical microcavities show an increase of about five orders of magnitude in electric current with respect to the same bare device. This feature can be used to sense volatile substances. PDIF-CN2 also improves chemical resistance of PSi against alkaline and acid corrosion. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Arbitrary Control of Polarization and Intensity Profiles of Diffraction-Attenuation-Resistant Beams along the Propagation Direction

Science.gov (United States)

Corato-Zanarella, Mateus; Dorrah, Ahmed H.; Zamboni-Rached, Michel; Mojahedi, Mo

2018-02-01

We report on the theory and experimental generation of a class of diffraction-attenuation-resistant beams with state of polarization (SOP) and intensity that can be controlled on demand along the propagation direction. This control is achieved by a suitable superposition of Bessel beams, whose parameters are systematically chosen based on closed-form analytic expressions provided by the frozen waves method. Using an amplitude-only spatial light modulator, we experimentally demonstrate three scenarios. In the first, the SOP of a horizontally polarized beam evolves to radial polarization and is then changed to vertical polarization, with the beam intensity held constant. In the second, we simultaneously control the SOP and the longitudinal intensity profile, which is chosen such that the beam's central ring can be switched off over predefined space regions, thus generating multiple foci with different SOPs and at different intensity levels along the propagation. Finally, the ability to control the SOP while overcoming attenuation inside lossy fluids is shown experimentally. We envision our proposed method to be of great interest for many applications, such as optical tweezers, atom guiding, material processing, microscopy, and optical communications.

Irradiation Testing of Ultrasonic Transducers

International Nuclear Information System (INIS)

Daw, J.; Rempe, J.; Palmer, J.; Tittmann, B.; Reinhardt, B.; Kohse, G.; Ramuhalli, P.; Montgomery, R.; Chien, H.T.; Villard, J.F.

2013-06-01

Ultrasonic technologies offer the potential for high accuracy and resolution in-pile measurement of numerous parameters, including geometry changes, temperature, crack initiation and growth, gas pressure and composition, and microstructural changes. Many Department of Energy-Office of Nuclear Energy (DOE-NE) programs are exploring the use of ultrasonic technologies to provide enhanced sensors for in-pile instrumentation during irradiation testing. For example, the ability of single, small diameter ultrasonic thermometers (UTs) to provide a temperature profile in candidate metallic and oxide fuel would provide much needed data for validating new fuel performance models. Other efforts include an ultrasonic technique to detect morphology changes (such as crack initiation and growth) and acoustic techniques to evaluate fission gas composition and pressure. These efforts are limited by the lack of existing knowledge of ultrasonic transducer material survivability under irradiation conditions. To address this need, the Pennsylvania State University (PSU) was awarded an Advanced Test Reactor National Scientific User Facility (ATR NSUF) project to evaluate promising magnetostrictive and piezoelectric transducer performance in the Massachusetts Institute of Technology Research Reactor (MITR) up to a fast fluence of at least 10 21 n/cm 2 (E> 0.1 MeV). This test will be an instrumented lead test; and real-time transducer performance data will be collected along with temperature and neutron and gamma flux data. By characterizing magnetostrictive and piezoelectric transducer survivability during irradiation, test results will enable the development of novel radiation tolerant ultrasonic sensors for use in Material and Test Reactors (MTRs). The current work bridges the gap between proven out-of-pile ultrasonic techniques and in-pile deployment of ultrasonic sensors by acquiring the data necessary to demonstrate the performance of ultrasonic transducers. (authors)

Amos-type bounds for modified Bessel function ratios☆

Science.gov (United States)

Hornik, Kurt; Grün, Bettina

2013-01-01

We systematically investigate lower and upper bounds for the modified Bessel function ratio Rν=Iν+1/Iν by functions of the form Gα,β(t)=t/(α+t2+β2) in case Rν is positive for all t>0, or equivalently, where ν≥−1 or ν is a negative integer. For ν≥−1, we give an explicit description of the set of lower bounds and show that it has a greatest element. We also characterize the set of upper bounds and its minimal elements. If ν≥−1/2, the minimal elements are tangent to Rν in exactly one point 0≤t≤∞, and have Rν as their lower envelope. We also provide a new family of explicitly computable upper bounds. Finally, if ν is a negative integer, we explicitly describe the sets of lower and upper bounds, and give their greatest and least elements, respectively. PMID:24926105

Amos-type bounds for modified Bessel function ratios.

Science.gov (United States)

Hornik, Kurt; Grün, Bettina

2013-12-01

We systematically investigate lower and upper bounds for the modified Bessel function ratio [Formula: see text] by functions of the form [Formula: see text] in case [Formula: see text] is positive for all [Formula: see text], or equivalently, where [Formula: see text] or [Formula: see text] is a negative integer. For [Formula: see text], we give an explicit description of the set of lower bounds and show that it has a greatest element. We also characterize the set of upper bounds and its minimal elements. If [Formula: see text], the minimal elements are tangent to [Formula: see text] in exactly one point [Formula: see text], and have [Formula: see text] as their lower envelope. We also provide a new family of explicitly computable upper bounds. Finally, if [Formula: see text] is a negative integer, we explicitly describe the sets of lower and upper bounds, and give their greatest and least elements, respectively.

Higher order Riesz transforms associated with Bessel operators

Science.gov (United States)

Betancor, Jorge J.; Fariña, Juan C.; Martinez, Teresa; Rodríguez-Mesa, Lourdes

2008-10-01

In this paper we investigate Riesz transforms R μ ( k) of order k≥1 related to the Bessel operator Δμ f( x)=- f”( x)-((2μ+1)/ x) f’( x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We obtain that for every k≥1, R μ ( k) is a principal value operator of strong type ( p, p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ( x)= x 2μ+1 dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R μ ( k) maps L p (ω) into itself and L 1(ω) into L 1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class mathcal{A}p^μ of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman.

A Novel Algorithm for the Sound Field of Elliptically Shaped Transducers

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Ding, De-Sheng; Lü, Hua; Shen, Chang-Sheng

2014-06-01

An alternative extension to the Gaussian-beam expansion technique is presented for efficient computation of the Fresnel field integral for elliptically symmetric sources. With a known result that the circ function is approximately decomposed into a sum of Gaussian functions, the cosine function is similarly expanded by the Bessel—Fourier transform. Two expansions are together inserted into this integral, it is then expressible in terms of the simple algebraic functions. The numerical examples for the elliptical and uniform piston transducers are presented, in good agreement with the results given by other methods. The approach is applicable to treat the field radiation problem for a large and important group of piston sources in acoustics.

Ultrasonic Transducer Peak-to-Peak Optical Measurement

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Pavel Skarvada

2012-01-01

Full Text Available Possible optical setups for measurement of the peak-to-peak value of an ultrasonic transducer are described in this work. The Michelson interferometer with the calibrated nanopositioner in reference path and laser Doppler vibrometer were used for the basic measurement of vibration displacement. Langevin type of ultrasonic transducer is used for the purposes of Electro-Ultrasonic Nonlinear Spectroscopy (EUNS. Parameters of produced mechanical vibration have to been well known for EUNS. Moreover, a monitoring of mechanical vibration frequency shift with a mass load and sample-transducer coupling is important for EUNS measurement.

Metaoptics for Spectral and Spatial Beam Manipulation

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Raghu Srimathi, Indumathi

Laser beam combining and beam shaping are two important areas with applications in optical communications, high power lasers, and atmospheric propagation studies. In this dissertation, metaoptical elements have been developed for spectral and spatial beam shaping, and multiplexing. Beams carrying orbital angular momentum (OAM), referred to as optical vortices, have unique propagation properties. Optical vortex beams carrying different topological charges are orthogonal to each other and have low inter-modal crosstalk which allows for them to be (de)multiplexed. Efficient spatial (de)multiplexing of these beams have been carried out by using diffractive optical geometrical coordinate transformation elements. The spatial beam combining technique shown here is advantageous because the efficiency of the system is not dependent on the number of OAM states being combined. The system is capable of generating coaxially propagating beams in the far-field and the beams generated can either be incoherently or coherently multiplexed with applications in power scaling and dynamic intensity profile manipulations. Spectral beam combining can also be achieved with the coordinate transformation elements. The different wavelengths emitted by fiber sources can be spatially overlapped in the far-field plane and the generated beams are Bessel-Gauss in nature with enhanced depth of focus properties. Unique system responses and beam shapes in the far-field can be realized by controlling amplitude, phase, and polarization at the micro-scale. This has been achieved by spatially varying the structural parameters at the subwavelength scale and is analogous to local modification of material properties. With advancements in fabrication technology, it is possible to control not just the lithographic process, but also the deposition process. In this work, a unique combination of spatial structure variations in conjunction with the conformal coating properties of an atomic layer deposition tool

Filtered Bessel functions in computerized tomography

International Nuclear Information System (INIS)

Rathore, R.K.S.; Munshi, P.; Bhatia, V.K.; Pandimani, S.

1988-01-01

Computer Aided Tomography (CAT) is widely used in the medical imaging area for the detection of cancerous tissues. It has also proved to be a good technique for measuring point-density (void-fraction) in two-phase flow systems. The present day CAT-scanners employ alogorithms which are essentially a discrete implementation of the Radon Inversion Formulae. These methods of reconstructing density distributions are fast and easy to implement. The present work is an attempt to simplify (and consequently to speed-up) the existing algorithms for the cases of radially symmetric density distribution. The method uses Radon Inversion Formulae and involves Bessels's Function of Fourier frequency. The algorithm was tested on some known distributions and the reconstruction is excellent. Data for bubbly-flow was also processed to obtain a point density distribution. The range of investigation was 0.6 ≤ ≤ 0.9 g/cm 3 , where ' ' denotes average cross-sectional value. The values of CT > are within ±0.03 g/cm 3 of the true values , for the data sets considered. The results are comparable with another simple method involving radial polynominals. It is observed that the simplified Radon Inversion Formulae for the radially symmetric case gives good results and can be implemented with ease. (orig.)

All-optical optoacoustic microscopy based on probe beam deflection technique

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Saher M. Maswadi

2016-09-01

Full Text Available Optoacoustic (OA microscopy using an all-optical system based on the probe beam deflection technique (PBDT for detection of laser-induced acoustic signals was investigated as an alternative to conventional piezoelectric transducers. PBDT provides a number of advantages for OA microscopy including (i efficient coupling of laser excitation energy to the samples being imaged through the probing laser beam, (ii undistorted coupling of acoustic waves to the detector without the need for separation of the optical and acoustic paths, (iii high sensitivity and (iv ultrawide bandwidth. Because of the unimpeded optical path in PBDT, diffraction-limited lateral resolution can be readily achieved. The sensitivity of the current PBDT sensor of 22 μV/Pa and its noise equivalent pressure (NEP of 11.4 Pa are comparable with these parameters of the optical micro-ring resonator and commercial piezoelectric ultrasonic transducers. Benefits of the present prototype OA microscope were demonstrated by successfully resolving micron-size details in histological sections of cardiac muscle.

All-optical optoacoustic microscopy based on probe beam deflection technique.

Science.gov (United States)

Maswadi, Saher M; Ibey, Bennett L; Roth, Caleb C; Tsyboulski, Dmitri A; Beier, Hope T; Glickman, Randolph D; Oraevsky, Alexander A

2016-09-01

Optoacoustic (OA) microscopy using an all-optical system based on the probe beam deflection technique (PBDT) for detection of laser-induced acoustic signals was investigated as an alternative to conventional piezoelectric transducers. PBDT provides a number of advantages for OA microscopy including (i) efficient coupling of laser excitation energy to the samples being imaged through the probing laser beam, (ii) undistorted coupling of acoustic waves to the detector without the need for separation of the optical and acoustic paths, (iii) high sensitivity and (iv) ultrawide bandwidth. Because of the unimpeded optical path in PBDT, diffraction-limited lateral resolution can be readily achieved. The sensitivity of the current PBDT sensor of 22 μV/Pa and its noise equivalent pressure (NEP) of 11.4 Pa are comparable with these parameters of the optical micro-ring resonator and commercial piezoelectric ultrasonic transducers. Benefits of the present prototype OA microscope were demonstrated by successfully resolving micron-size details in histological sections of cardiac muscle.

Piezoelectric Nanotube Array for Broadband High-Frequency Ultrasonic Transducer.

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Liew, Weng Heng; Yao, Kui; Chen, Shuting; Tay, Francis Eng Hock

2018-03-01

Piezoelectric materials are vital in determining ultrasonic transducer and imaging performance as they offer the function for conversion between mechanical and electrical energy. Ultrasonic transducers with high-frequency operation suffer from performance degradation and fabrication difficulty of the demanded piezoelectric materials. Hence, we propose 1-D polymeric piezoelectric nanostructure with controlled nanoscale features to overcome the technical limitations of high-frequency ultrasonic transducers. For the first time, we demonstrate the integration of a well-aligned piezoelectric nanotube array to produce a high-frequency ultrasonic transducer with outstanding performance. We find that nanoconfinement-induced polarization orientation and unique nanotube structure lead to significantly improved piezoelectric and ultrasonic transducing performance over the conventional piezoelectric thin film. A large bandwidth, 126% (-6 dB), is achieved at high center frequency, 108 MHz. Transmission sensitivity of nanotube array is found to be 46% higher than that of the monolithic thin film transducer attributed to the improved electromechanical coupling effectiveness and impedance match. We further demonstrate high-resolution scanning, ultrasonic imaging, and photoacoustic imaging using the obtained nanotube array transducers, which is valuable for biomedical imaging applications in the future.